Factoring Tutorial by Wesley Dugan

First of all we first need to know what factoring is before we can attempt to factor trinomials.

Factoring: A process used to write a polynomial as a product of other polynomials having equal or lesser degree.

What we will be learning about factoring is:

- Difference of two squares

- Perfect square trinomials

- Any trinomial written in standard form

- Trinomials that have a common factor to take out first

Difference of two squares:

Pattern: a^2 – b^2 = (a + b)(a - b)

Example: x^2 – 9

First what you want to do is see what times itself gets x^2. In this case it is x. So put x in the a spot. Now see what times itself gets 9.

It is 3. So put it in the b spot. In the end you will get… x^2 – 9 factors to (x + 3)(x - 3). To check your answer x times x is x^2 and 3 times -3 is -9.

Perfect square trinomials:

Pattern a^2 + 2ab + b^2 = (a + b)^2

Example: x^2 + 14x + 49

First we know this is a perfect square trinomial. The first and last numbers need to be square rooted. The square root of x^2 is x. So put x in the a spot. Second the square root of 49 is 7. So put 7 in the b spot. Your final answer will be (x + 7)^2. To check the answer just solve it… x times x is x^2, 7x + 7x is 14x, and 7 times 7 is 49 or x^2 + 14x +49.

Any trinomial written in standard form:

The standard form of a trinomial is ax^2 + bx + c = 0. These types of equations can be solved using the zero product property. The zero product property states… Let A and B be real numbers or algebraic expressions. If AB = 0, then A = 0 or B = 0.

Example: x^2 – 3x – 18 = 0

First we factor it. We get (x + 6)(x - 3) = 0. Here we want to solve for the first variable… x + 6 = 0. Our first variable equals -6. To get out second variable we solve x - 3 = 0. Our second variable is 3. So x can either be -6 or 3.

Practice Problems:

1. x^2 – 16

2. x^2 + 16x + 64

3. x^2 + 9x + 14