Using Factoring

Key Information Topic B:

• Using Factoring
• First Step - Multiplying Binomials
• Factoring a Quadratic

 

Factoring quadratics is used for the following:

1. Finding the  x and y intercepts
2. Finding the vertex (highest or lowest point)
3. Solving problems using methods of factoring (using distributive method or foil, completing a square, the quadratic formula)

Before exploring quadratics further, we need to understand the elements or parts of a factored quadratic. Factoring means that you are simplifying a product. By factoring in Algebra, what we mean is that you are taking the product or “quadratic expression” and examining the factors that make up the quadratic.

Let us start with a simpler example of factoring…
Factors of 6 are (2) (3)

When you factor a quadratic equation, you end up with binomials as your factors. Binomials are the factors of a quadratic equation.

A binomial is simply the addition or subtraction of two terms. In this case, with quadratic equations, a binomial includes two terms a variable and a number or two numbers, or two variables. The following are examples of binomials:

(x+3)
(2+1)
(x+y)
(z³+7)

In the examples of quadratic equations in this course, you will see only binomials that have a variable and a number, and the variable only has the power of 1. Therefore, the binomial format will look like this:

(x+a)…. (x+12)  or
(x-a)….. (x-1)