{"id":911,"date":"2016-02-15T20:59:28","date_gmt":"2016-02-15T20:59:28","guid":{"rendered":"https:\/\/courses.candelalearning.com\/nrocarithmetic\/?post_type=chapter&p=911"},"modified":"2026-02-01T07:15:16","modified_gmt":"2026-02-01T07:15:16","slug":"4-2-2-adding-and-subtracting-polynomials","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-elementaryalgebra\/chapter\/4-2-2-adding-and-subtracting-polynomials\/","title":{"raw":"5.5: Adding and Subtracting Polynomials","rendered":"5.5: Adding and Subtracting Polynomials"},"content":{"raw":"
\r\n

section 5.5 Learning Objectives<\/h3>\r\n5.5: Adding and Subtracting Polynomials<\/strong>\r\n
    \r\n \t
  • Add polynomials<\/li>\r\n \t
  • Find the opposite of a polynomial<\/li>\r\n \t
  • Subtract polynomials<\/li>\r\n<\/ul>\r\n<\/div>\r\n \r\n

    Adding polynomials<\/h2>\r\nAdding and subtracting polynomials<\/b> may sound complicated, but it\u2019s really not much different from the addition and subtraction that you do every day. The main thing to remember is to look for and combine like terms<\/b>. You can add two (or more) polynomials as you have added algebraic expressions. You can remove the parentheses and combine like terms.\r\n
    \r\n

    Example 1<\/h3>\r\nAdd the following two binomials. [latex]\\left(3b+5\\right)+\\left(2b+4\\right)[\/latex]\r\n\r\n[reveal-answer q=\"379821\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"379821\"]Regroup\r\n

    [latex]\\left(3b+2b\\right)+\\left(5+4\\right)[\/latex]<\/p>\r\nCombine like terms.\r\n

    [latex]5b + 9[\/latex]<\/p>\r\n\r\n

    Answer<\/h4>\r\n[latex]\\left(3b+5\\right)+\\left(2b+4\\right)=5b+9[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nWhen you are adding polynomials that have subtraction,\u00a0it is important to remember to keep the sign on each term as you are collecting like terms. \u00a0 The next example will show you how to regroup terms that are subtracted when you are collecting like terms.\r\n
    \r\n

    Example 2<\/h3>\r\nAdd. [latex]\\left(-5x^{2}\u201310x+2\\right)+\\left(3x^{2}+7x\u20134\\right)[\/latex]\r\n\r\n[reveal-answer q=\"486380\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"486380\"]\r\n\r\nCollect like terms, making sure you keep the sign on each term. For example, when you collect\u00a0the [latex]x^2[\/latex] terms, make sure to keep the negative sign on [latex]-5x^2[\/latex].\r\n\r\nHelpful Hint: We find that it is easier to put the terms with a negative sign on the right of the terms that are positive. This would mean\u00a0that the\u00a0[latex]x^2[\/latex] terms would be grouped as\u00a0[latex]\\left(3x^{2}-5x^{2}\\right)[\/latex]. If both terms are negative, then it doesn't matter which is on the left or right.\r\n\r\nThe polynomial now looks like this, with like terms collected:\r\n

    [latex]\\begin{array}{c}\\underbrace{\\left(3x^{2}-5x^{2}\\right)}+\\underbrace{\\left(7x-10x\\right)}+\\underbrace{\\left(2-4\\right)}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,x^2\\text{ terms }\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,x\\text{ terms}\\,\\,\\,\\,\\,\\,\\,\\,\\text{ constants }\\end{array}[\/latex]<\/p>\r\n

    The [latex]x^2[\/latex] terms will simplify to [latex]-2x^{2}[\/latex]<\/p>\r\n

    The\u00a0[latex]x[\/latex] will simplify to [latex]-3x[\/latex]<\/p>\r\n

    The constant terms will simplify to [latex]-2[\/latex]<\/p>\r\n

    \u00a0Rewrite the polynomial with it's simplified terms, keeping the sign on each term.<\/p>\r\n

    [latex]-2x^{2}-3x-2[\/latex]<\/p>\r\n

    As a matter of convention, we write polynomials in descending order based on degree. \u00a0Notice how we put the\u00a0[latex]x^2[\/latex] term first, the\u00a0[latex]x[\/latex] term second and the constant term last.<\/p>\r\n\r\n

    Answer<\/h4>\r\n[latex]\\left(-5x^{2}-10x+2\\right)+\\left(3x^{2}+7x-4\\right)=-2x^{2}-3x-2[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe above examples show addition of polynomials horizontally, by reading from left to right along the same line. Some people like to organize their work vertically instead, because they find it easier to be sure that they are combining like terms. The example below shows this \u201cvertical\u201d method of adding polynomials:\r\n
    \r\n

    Example 3<\/h3>\r\nAdd. [latex]\\left(3x^{2}+2x-7\\right)+\\left(7x^{2}-4x+8\\right)[\/latex]\r\n\r\n[reveal-answer q=\"425224\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"425224\"]Write one polynomial below the other, making sure to line up like terms.\r\n

    [latex]\\begin{array}{r}3x^{2}+2x-7\\\\+7x^{2}-4x+8\\end{array}[\/latex]<\/p>\r\nCombine like terms, paying close attention to the signs.\r\n

    [latex]\\begin{array}{r}3x^{2}+2x-7\\\\\\underline{+7x^{2}-4x+8}\\\\10x^{2}-2x+1\\end{array}[\/latex]\u00a0<\/b><\/p>\r\n\r\n

    Answer<\/h4>\r\n[latex]\\left(3x^{2}+2x-7\\right)+\\left(7x^{2}-4x+8\\right)=10x^{2}-2x+1[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nSometimes in a vertical arrangement, you can line up every term beneath a like term, as in the example above. But sometimes it isn't so tidy. When there isn't a matching like term for every term, there will be empty places in the vertical arrangement.\r\n
    \r\n

    Example 4<\/h3>\r\nAdd. [latex]\\left(4x^{3}+5x^{2}-6x+2\\right)+\\left(-4x^{2}+10\\right)[\/latex]\r\n\r\n[reveal-answer q=\"232680\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"232680\"]Write one polynomial below the other, lining up like terms vertically.\r\n\r\nTo keep track of like terms, you can insert zeros where there aren't any shared like terms. This is optional, but some find it helpful.\r\n

    [latex]\\begin{array}{r}4x^{3}+5x^{2}-6x+2\\\\+0\\,\\,-4x^{2}\\,\\,+0\\,\\,+10\\end{array}[\/latex]<\/p>\r\nCombine like terms, paying close attention to the signs.\r\n

    [latex]\\begin{array}{r}4x^{3}+5x^{2}-6x+\\,\\,\\,2\\\\\\underline{+0\\,\\,-4x^{2}\\,\\,+0\\,\\,+10}\\\\4x^{3}\\,+\\,\\,x^{2}-6x+12\\end{array}[\/latex]<\/p>\r\n\r\n

    Answer<\/h4>\r\n[latex]\\left(4x^{3}+5x^{2}-6x+2\\right)+\\left(-4x^{2}+10\\right)=4x^{3}+x^{2}-6x+12[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nYou may be thinking, how is this different than combining like terms, which we did in the last section? The answer is, it's not really. We just added a layer to combining like terms by adding more terms to combine.\u00a0 Polynomials are a useful tool for describing the behavior of anything that isn't linear, and sometimes you may need to add them.\r\n\r\nIn the following video, you will see more examples of combining like terms by adding polynomials.\r\n\r\nhttps:\/\/youtu.be\/KYZR7g7QcF4\r\n

    Find the opposite of a polynomial<\/h2>\r\n\"ScaleWhen you are solving equations, it may come up that you need to subtract polynomials. This means subtracting each term of a polynomial, which requires\u00a0changing the sign of each term in a polynomial. Recall that changing the sign\u00a0of 3 gives [latex]\u22123[\/latex], and changing the sign\u00a0of [latex]\u22123[\/latex] gives 3. Just as changing the sign\u00a0of a number is found by multiplying the number by [latex]\u22121[\/latex], we can change the sign\u00a0of a polynomial by multiplying it by [latex]\u22121[\/latex]. Think of this in the same way as you would the distributive property. \u00a0You are distributing [latex]\u22121[\/latex] to each term in the polynomial. \u00a0Changing the sign of a polynomial is also called finding the opposite.\r\n
    \r\n

    Example 5<\/h3>\r\nFind the opposite of [latex]9x^{2}+10x+5[\/latex].\r\n\r\n[reveal-answer q=\"161313\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"161313\"]Find the opposite by multiplying by [latex]\u22121[\/latex].\r\n

    [latex]\\left(-1\\right)\\left(9x^{2}+10x+5\\right)[\/latex]<\/p>\r\nDistribute [latex]\u22121[\/latex] to each term in the polynomial.\r\n

    [latex]\\left(-1\\right)9x^{2}+\\left(-1\\right)10x+\\left(-1\\right)5[\/latex]<\/p>\r\nYour new terms all have the opposite sign:\r\n

    [latex]\\begin{array}{c}\\left(-1\\right)9x^{2}=-9x^{2}\\\\\\text{ }\\\\\\left(-1\\right)10x=-10x\\\\\\text{ }\\\\\\left(-1\\right)5=-5\\end{array}[\/latex]<\/p>\r\nNow you can rewrite the polynomial with the new sign on each term:\r\n

    [latex]-9x^{2}-10x-5[\/latex]<\/p>\r\n\r\n

    Answer<\/h4>\r\nThe opposite of [latex]9x^{2}+10x+5[\/latex] is [latex]-9x^{2}-10x-5[\/latex]\r\n\r\nYou can also write:\r\n\r\n[latex]\\left(-1\\right)\\left(9x^{2}+10x+5\\right)=-9x^{2}-10x-5[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n
    \"Caution\"Be careful when there are negative terms\u00a0or subtractions in the polynomial already. \u00a0Just remember that you are changing the sign, so if it is negative, it will become positive.<\/div>\r\n
    \r\n

    Example 6<\/h3>\r\nFind the opposite of [latex]3p^{2}\u20135p+7[\/latex].\r\n\r\n[reveal-answer q=\"278382\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"278382\"]Find the opposite by multiplying by [latex]-1[\/latex].\r\n

    [latex]\\left(-1\\right)\\left(3p^{2}-5p+7\\right)[\/latex]<\/p>\r\nDistribute [latex]-1[\/latex] to each term in the polynomial by multiplying each coefficient by [latex]-1[\/latex].\r\n

    [latex]\\left(-1\\right)3p^{2}+\\left(-1\\right)\\left(-5p\\right)+\\left(-1\\right)7[\/latex]<\/p>\r\nYour new terms all have the opposite sign:\r\n

    [latex]\\begin{array}{c}\\left(-1\\right)3p^{2}=-3p^{2}\\\\\\text{ }\\\\\\left(-1\\right)\\left(-5p\\right)=5p\\\\\\text{ }\\\\\\left(-1\\right)7=-7\\end{array}[\/latex]<\/p>\r\n

    Now you can rewrite the polynomial with the new sign on each term:<\/p>\r\n

    [latex]-3p^{2}+5p-7[\/latex]<\/p>\r\n\r\n

    Answer<\/h4>\r\nThe opposite of [latex]3p^{2}-5p+7[\/latex] is [latex]-3p^{2}+5p-7[\/latex].\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNotice that in finding the opposite of a polynomial, you change the sign of each term<\/i> in the polynomial, then rewrite the polynomial with the new signs on each term.\r\n

    Subtracting polynomials<\/h2>\r\nWhen you subtract one polynomial from another, you will first find the opposite of the polynomial being subtracted, then combine like terms. The easiest mistake to make when subtracting one polynomial from another is to forget to change the sign of EVERY term in the polynomial being subtracted.\r\n
    \r\n

    Example 7<\/h3>\r\nSubtract. [latex]\\left(15x^{2}+12x+20\\right)\u2013\\left(9x^{2}+10x+5\\right)[\/latex]\r\n\r\n[reveal-answer q=\"267023\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"267023\"]Change\u00a0the sign of each<\/i> term in the polynomial [latex]9x^{2}+10x+5[\/latex]. All the terms are positive, so they will all become negative.\r\n

    [latex]\\left(15x^{2}+12x+20\\right)-9x^{2}-10x-5[\/latex]<\/p>\r\nRegroup to match like terms, remember to check\u00a0the sign of each term.\r\n

    [latex]15x^{2}-9x^{2}+12x-10x+20-5[\/latex]<\/p>\r\nCombine like terms.\r\n

    [latex]6x^{2}+2x+15[\/latex]<\/p>\r\n\r\n

    Answer<\/h4>\r\n[latex]\\left(15x^{2}+12x+20\\right)-\\left(9x^{2}+10x+5\\right)=6x^{2}+2x+15[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n
    \"Caution\"When polynomials include a lot of terms, it can be easy to lose track of the signs. Be careful to transfer them correctly, especially when subtracting a negative term.<\/div>\r\n
    \r\n

    Example 8<\/h3>\r\nSubtract. [latex]\\left(14x^{3}+3x^{2}\u20135x+14\\right)\u2013\\left(7x^{3}+5x^{2}\u20138x+10\\right)[\/latex]\r\n\r\n[reveal-answer q=\"783926\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"783926\"]Change the sign of each term in the polynomial [latex]7x^{3}+5x^{2}\u20138x+10[\/latex]\r\n

    [latex]\\left(14x^{3}+3x^{2}-5x+14\\right)-7x^{3}-5x^{2}+8x-10[\/latex]<\/p>\r\nRegroup to put like terms together and combine like terms.\r\n

    [latex]\\begin{array}{c}\\underbrace{14x^{3}-7x^{3}}+\\underbrace{3x^{2}-5x^{2}}-\\underbrace{5x+8x}+\\underbrace{14-10}\\\\=7x^{3}\\,\\,\\,\\,\\,\\,\\,\\,\\,=-2x^{2}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=3x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=4\\end{array}[\/latex]<\/p>\r\n

    Write the resulting polynomial with each term's sign in front.<\/p>\r\n

    [latex]7x^{3}-2x^{2}+3x+4[\/latex]<\/p>\r\n\r\n

    Answer<\/h4>\r\n[latex]\\left(14x^{3}+3x^{2}-5x+14\\right)-\\left(7x^{3}+5x^{2}-8x+10\\right)=7x^{3}-2x^{2}+3x+4[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nWhen you have many terms,\u00a0like in the example above, try the vertical approach from the previous page to keep your terms organized. \u00a0However you choose to combine polynomials is up to you\u2014the key point is to identify like terms, keep track of their signs, and be able to organize them accurately.\r\n
    \r\n

    Example 9<\/h3>\r\nSubtract. [latex]\\left(14x^{3}+3x^{2}\u20135x+14\\right)\u2013\\left(7x^{3}+5x^{2}\u20138x+10\\right)[\/latex]\r\n\r\n[reveal-answer q=\"29114\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"29114\"]Reorganizing using the vertical approach.\r\n

    [latex]14x^{3}+3x^{2}-5x+14-\\left(7x^{3}+5x^{2}-8x+10\\right)[\/latex]<\/p>\r\nChange the signs, and combine like terms.\r\n

    [latex]\\begin{array}{l}14x^{3}+3x^{2}-5x+14\\,\\,\\,\\,\\\\\\underline{-7x^{3}-5x^{2}+8x-10}\\\\=7x^{3}-2x^{2}+3x+4\\,\\,\\,\\end{array}[\/latex]<\/p>\r\n\r\n

    Answer<\/h4>\r\n[latex]\\left(14x^{3}+3x^{2}-5x+14\\right)-\\left(7x^{3}+5x^{2}-8x+10\\right)=7x^{3}-2x^{2}+3x+4[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following video, you will see more examples of subtracting polynomials.\r\n\r\nhttps:\/\/youtu.be\/xq-zVm25VC0\r\n

    Summary<\/h2>\r\nWe have seen that subtracting a polynomial means changing the sign of each term in the polynomial and then reorganizing all the terms to make it easier to combine those that are alike. \u00a0How you organize this process is up to you, but we have shown two ways here. \u00a0One method is to place the terms next to each other horizontally, putting like terms next to each other to make combining them easier. \u00a0The other method was to place the polynomial being subtracted underneath the other after changing the signs of each term. In this method it is important to align like terms and use a blank space when there is no like term.","rendered":"
    \n

    section 5.5 Learning Objectives<\/h3>\n

    5.5: Adding and Subtracting Polynomials<\/strong><\/p>\n

      \n
    • Add polynomials<\/li>\n
    • Find the opposite of a polynomial<\/li>\n
    • Subtract polynomials<\/li>\n<\/ul>\n<\/div>\n

       <\/p>\n

      Adding polynomials<\/h2>\n

      Adding and subtracting polynomials<\/b> may sound complicated, but it\u2019s really not much different from the addition and subtraction that you do every day. The main thing to remember is to look for and combine like terms<\/b>. You can add two (or more) polynomials as you have added algebraic expressions. You can remove the parentheses and combine like terms.<\/p>\n

      \n

      Example 1<\/h3>\n

      Add the following two binomials. [latex]\\left(3b+5\\right)+\\left(2b+4\\right)[\/latex]<\/p>\n

      Show Solution<\/span><\/p>\n
      Regroup<\/p>\n

      [latex]\\left(3b+2b\\right)+\\left(5+4\\right)[\/latex]<\/p>\n

      Combine like terms.<\/p>\n

      [latex]5b + 9[\/latex]<\/p>\n

      Answer<\/h4>\n

      [latex]\\left(3b+5\\right)+\\left(2b+4\\right)=5b+9[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n

      When you are adding polynomials that have subtraction,\u00a0it is important to remember to keep the sign on each term as you are collecting like terms. \u00a0 The next example will show you how to regroup terms that are subtracted when you are collecting like terms.<\/p>\n

      \n

      Example 2<\/h3>\n

      Add. [latex]\\left(-5x^{2}\u201310x+2\\right)+\\left(3x^{2}+7x\u20134\\right)[\/latex]<\/p>\n

      Show Solution<\/span><\/p>\n
      \n

      Collect like terms, making sure you keep the sign on each term. For example, when you collect\u00a0the [latex]x^2[\/latex] terms, make sure to keep the negative sign on [latex]-5x^2[\/latex].<\/p>\n

      Helpful Hint: We find that it is easier to put the terms with a negative sign on the right of the terms that are positive. This would mean\u00a0that the\u00a0[latex]x^2[\/latex] terms would be grouped as\u00a0[latex]\\left(3x^{2}-5x^{2}\\right)[\/latex]. If both terms are negative, then it doesn’t matter which is on the left or right.<\/p>\n

      The polynomial now looks like this, with like terms collected:<\/p>\n

      [latex]\\begin{array}{c}\\underbrace{\\left(3x^{2}-5x^{2}\\right)}+\\underbrace{\\left(7x-10x\\right)}+\\underbrace{\\left(2-4\\right)}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,x^2\\text{ terms }\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,x\\text{ terms}\\,\\,\\,\\,\\,\\,\\,\\,\\text{ constants }\\end{array}[\/latex]<\/p>\n

      The [latex]x^2[\/latex] terms will simplify to [latex]-2x^{2}[\/latex]<\/p>\n

      The\u00a0[latex]x[\/latex] will simplify to [latex]-3x[\/latex]<\/p>\n

      The constant terms will simplify to [latex]-2[\/latex]<\/p>\n

      \u00a0Rewrite the polynomial with it’s simplified terms, keeping the sign on each term.<\/p>\n

      [latex]-2x^{2}-3x-2[\/latex]<\/p>\n

      As a matter of convention, we write polynomials in descending order based on degree. \u00a0Notice how we put the\u00a0[latex]x^2[\/latex] term first, the\u00a0[latex]x[\/latex] term second and the constant term last.<\/p>\n

      Answer<\/h4>\n

      [latex]\\left(-5x^{2}-10x+2\\right)+\\left(3x^{2}+7x-4\\right)=-2x^{2}-3x-2[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n

      The above examples show addition of polynomials horizontally, by reading from left to right along the same line. Some people like to organize their work vertically instead, because they find it easier to be sure that they are combining like terms. The example below shows this \u201cvertical\u201d method of adding polynomials:<\/p>\n

      \n

      Example 3<\/h3>\n

      Add. [latex]\\left(3x^{2}+2x-7\\right)+\\left(7x^{2}-4x+8\\right)[\/latex]<\/p>\n

      Show Solution<\/span><\/p>\n
      Write one polynomial below the other, making sure to line up like terms.<\/p>\n

      [latex]\\begin{array}{r}3x^{2}+2x-7\\\\+7x^{2}-4x+8\\end{array}[\/latex]<\/p>\n

      Combine like terms, paying close attention to the signs.<\/p>\n

      [latex]\\begin{array}{r}3x^{2}+2x-7\\\\\\underline{+7x^{2}-4x+8}\\\\10x^{2}-2x+1\\end{array}[\/latex]\u00a0<\/b><\/p>\n

      Answer<\/h4>\n

      [latex]\\left(3x^{2}+2x-7\\right)+\\left(7x^{2}-4x+8\\right)=10x^{2}-2x+1[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n

      Sometimes in a vertical arrangement, you can line up every term beneath a like term, as in the example above. But sometimes it isn’t so tidy. When there isn’t a matching like term for every term, there will be empty places in the vertical arrangement.<\/p>\n

      \n

      Example 4<\/h3>\n

      Add. [latex]\\left(4x^{3}+5x^{2}-6x+2\\right)+\\left(-4x^{2}+10\\right)[\/latex]<\/p>\n

      Show Solution<\/span><\/p>\n
      Write one polynomial below the other, lining up like terms vertically.<\/p>\n

      To keep track of like terms, you can insert zeros where there aren’t any shared like terms. This is optional, but some find it helpful.<\/p>\n

      [latex]\\begin{array}{r}4x^{3}+5x^{2}-6x+2\\\\+0\\,\\,-4x^{2}\\,\\,+0\\,\\,+10\\end{array}[\/latex]<\/p>\n

      Combine like terms, paying close attention to the signs.<\/p>\n

      [latex]\\begin{array}{r}4x^{3}+5x^{2}-6x+\\,\\,\\,2\\\\\\underline{+0\\,\\,-4x^{2}\\,\\,+0\\,\\,+10}\\\\4x^{3}\\,+\\,\\,x^{2}-6x+12\\end{array}[\/latex]<\/p>\n

      Answer<\/h4>\n

      [latex]\\left(4x^{3}+5x^{2}-6x+2\\right)+\\left(-4x^{2}+10\\right)=4x^{3}+x^{2}-6x+12[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n

      You may be thinking, how is this different than combining like terms, which we did in the last section? The answer is, it’s not really. We just added a layer to combining like terms by adding more terms to combine.\u00a0 Polynomials are a useful tool for describing the behavior of anything that isn’t linear, and sometimes you may need to add them.<\/p>\n

      In the following video, you will see more examples of combining like terms by adding polynomials.<\/p>\n