# Factoring Polynomials: ax²+bx+c

This packet helps students understand how to factor more advanced quadratic equations. Students will use factoring to find the two solutions (also called roots or x-intercepts) of a quadratic equation (which graphs as a parabola). Factoring is the process of finding two terms -- for quadratic equations those terms will be two binomials -- that can be multiplied together to get the quadratic equation.

Many students are familiar with using the FOIL process to multiply binomials. Factoring quadratic equations is, essential, the reverse of using FOIL to turn a pair of binomials into a polynomial. For example:

If you are given the problem:$(x-2)(x+4)$

You would use FOIL (which stands for "multiply the FIRST terms, then the OUTER terms, then the INNER terms, then the LAST terms") to get: $x^2+4x-2x-8$,

which can be simplified to $x^2 +2x-8$

On the other hand, If you were given the expression $x^2 +2x-8$ and asked to factor it

(or if you were given $x^2 +2x-8$=0 and asked to solve it),

you would determine that:

$x \times x = x^2$, and $-2 \times 4 = -8$ *while* $-2+4=2$,

so $x^2 +2x-8 = (x-2)(x+4)$

Each page starts with easier problems that get more difficult as students work through the packet. Simpler problems are in standard form. More advanced problems require students to simplify and combine like terms before they factor the problem.

After doing all 36 problems, students should be more comfortable doing these problems and have a clear understanding of how to solve them.

Simple:

*Factor each polynomial.*

$2x²+3x+1$

Advanced:

*Solve each equation by factoring.*

$6x²+4x+4=-6x$

Practice problems require knowledge of addition, subtraction, multiplication, and division of integers.