Caddell Prep Access Menu

Factoring Quadratics

In this video, we are going to look at how to factor quadratics.
Quadratics are written in the form ax^2+bx+c. When factoring these, it will be split into two binomials, both of which will begin with x (when a is 1), and have the second terms add up to equal b, and multiply to equal c
For example:
To factor x^2+6x+8 we have to first write two sets of parentheses beginning with an x. Then, we have find two numbers that will add up to equal 6, and multiply to equal 8. These two numbers are 2 and 4, so when we factor this quadratic, we get
(x+2)(x+4)

To factor x^2-6x+8 we solve in the same way, only now b is negative. If two numbers add up to be negative, but multiply to be positive then we know that both numbers are going to be negative. These two numbers are -4 and -2, so when we factor this quadratic, we get
(x-4)(x-2)

To factor x^2+5x-6 we solve in the same way, only now c is negative. If two numbers add up to be positive, but multiply to be negative then we know the signs have to be different. These two numbers are 6 and -1, so when we factor this quadratic, we get
(x+6)(x-1)

*Note that when the signs are different, the number with the larger absolute value will have the same sign as the middle term of the quadratic.

To factor x^2-4x-21 we solve in the same way, only now both b and c are negative. If two numbers add up to be negative, and multiply to be negative then we know the signs have to be different. These two numbers are -7 and 3, so when we factor this quadratic, we get
(x-7)(x+3)

  • Want full access to all of our free math tutorials & practice problems?

    Used by students across the country. Pre-Algebra, Algebra I, Geometry, & Algebra II
    Sign Up Now