Expanding and Factoring Polynomials Review

Expanding and factoring were already covered in grade 9 but on a very surface level. You mainly operated with expressions in the form x^2 + bx + c, but obviously countless other forms. In this grade, you will learn about more of these forms along with some special polynomials with shortcuts to solve. These polynomials include:

ax^2 + bc + c

a^2 - b^2

a^2 + 2ab + b^2

To review, factoring means to write a number or expression as a product of terms, and x^2 + bx + c can be factored into the form (x + b)(x + c). To do this, you begin by setting up brackets:

(x + _)(x + _).

You will then try to find the two numbers that add to the value of b and multiply to the value of c.

Example:

x^2 - 21x + 90

= [x + (-6)][x + (-15)]

= (x - 6)(x - 15)

(-6) + (-15) = -21

(-6)(-15) = 90

Expanding polynomials is basically the opposite of factoring, where you are given two polynomials to multiply together instead of a large one to pull apart. With two binomials, often in the form (ax + b)(cx + d), we use the FOIL process, that has us multiply terms in the order:

First

Outer

Inner

Last

Example:

(2x + 4)(3x + 5)

First: (2x + 4)(3x + 5)

(2x)(3x) = 6x^2

Outer: (2x + 4)(3x + 5)

(2x)(5) = 10x

Inner: (2x + 4)(3x + 5)

(4)(3x) = 12x

Last: (2x + 4)(3x + 5)

(4)(5) = 20

Putting it all together and like terms:

6x^2 + 10x + 12x + 20

= 6x^2 + 22x + 20

(Remember to always write answer in order of descending powers)