Summary: Polynomial Basics

Key Equations

perfect square trinomial	[latex]{\left(x+a\right)}^{2}=\left(x+a\right)\left(x+a\right)={x}^{2}+2ax+{a}^{2}[/latex]
difference of squares	[latex]\left(a+b\right)\left(a-b\right)={a}^{2}-{b}^{2}[/latex]

A polynomial is a sum of terms each consisting of a variable raised to a nonnegative integer power. The degree is the highest power of the variable that occurs in the polynomial. The leading term is the term containing the highest degree, and the leading coefficient is the coefficient of that term.
We can add and subtract polynomials by combining like terms.
To multiply polynomials, use the distributive property to multiply each term in the first polynomial by each term in the second. Then add the products.
FOIL (First, Outer, Inner, Last) is a shortcut that can be used to multiply binomials.
Perfect square trinomials and difference of squares are special products.
Follow the same rules to work with polynomials containing several variables.

coefficient: any real number [latex]{a}_{i}[/latex] in a polynomial of the form [latex]{a}_{n}{x}^{n}+\dots+{a}_{2}{x}^{2}+{a}_{1}x+{a}_{0}[/latex]

difference of squares: the binomial that results when a binomial is multiplied by a binomial with the same terms, but the opposite sign

perfect square trinomial: the trinomial that results when a binomial is squared



polynomial: a sum of terms each consisting of a variable raised to a nonnegative integer power

term of a polynomial: any [latex]{a}_{i}{x}^{i}[/latex] of a polynomial of the form [latex]{a}_{n}{x}^{n}+\dots+{a}_{2}{x}^{2}+{a}_{1}x+{a}_{0}[/latex]