What you’ll learn to do: Use factoring methods to find the binomial factors of a polynomial.
One of the most important and powerful concepts that we use in mathematics is that of complementary operations. We already learned that subtraction can “undo” addition, and multiplication can “undo” division. These ideas helped us solve equations, find the slope of a line, and write a two variable linear equation iso that we could graph it easily. In the last unit, we learned that the techniques we learned for solving linear equations didn’t apply to solving polynomial equations, so we factored the polynomials and used the zero products principle. So far, we’ve worked with polynomials that factored into the product of a monomial and a binomial. In this section we will focus on learning how to factor a polynomial that results in the product of two binomials. Factoring “undoes” multiplication of polynomials.
Specifically, in this section you’ll learn how to:
- Factor a four term polynomial by grouping terms
- Apply an algorithm to rewrite a trinomial as a four term polynomial
- Using factoring by grouping to factor a trinomial
- Factor trinomials of the form [latex]ax^2+bx+c[/latex]
- Factor a trinomial with a leading coefficient of 1
- Use a shortcut to factor trinomials of the form [latex]x^2+bx+c[/latex]