Factoring Polynomials

Using the Distributive Property

First, find the GCF (Greatest Common Factor) of each term.

Then, rewrite each term using the GCF.

Then use the distributive property.

Example:

Factor 24 x² + 16 x · y

24 x² = 2 ·  2 ·  2 ·  3 ·  x ·  x

16y = 2 ·  2 ·  2 ·  2  · x · y

The GCF is 8x

8x (3x) + 8x(2y)

8x(3x + 2y)

By Grouping (Polynomials Having Four or More Terms)

First, group terms with common factors.

Then, factor the GCF from each groupng.

Then, apply the Distributive Property.

Example:

40a - 24ab + 3b - 5

Group terms with like factors: 40a - 5ab + 3b - 24 = (40a -5) - (24ab - 3b)

Factor GCF from each grouping: 5(8a - 1) - 3b(8a - 1)

Apply Distributive Property: (8a - 1)(-3b + 5)

Using the Additive Inverse Property

Example:

24x - 4xy + 7y - 42

Group terms with common factors: (24x - 4xy) + (7y - 42)

Find the GCF for each grouping: 4x(- y + 6) + 7(y - 6)

Apply the Additive Inverse Property to the first term:

- 4x(y - 6) + 7(y - 6)

Apply the Distributive Property: (y - 6)( - 4x + 7)

Solve Equations By Factoring

For any real numbers, if ab = 0 then either a = o, or b = 0.

Solve: x² = 5x

x² - 5x = 0

x(x - 5) = 0

Either x = 0, or (x - 5) = 0, and x = 5

The solution set is {0,5}