A quadratic equation is an equation that has an x² and is equal to 0. On a graph, the lines will look like a v. This is because, when solved, this equation will have two answers. There are 3 ways to solve a quadratic equation, I’ll be showing how to use one of them, factoring.

Now, we have a couple of questions we must ask ourselves when factoring.

Is there anything in common? Remove it.

15x³ – 5x²

5x²(3x – 1)

Is it a difference of squares?

There is a difference of 3x and 1, but they are not both squares.

25x²-49 would be a difference of squares that could then be factored.

25x²-49

(5x – 7)(5x + 7)

If we are still left with factorable terms, and there are three terms left, is there a pattern? Is it easy to factor or hard?

The pattern we look for is ax² + bx + c

If a = 1, it is easy to factor and we just need two terms that have the product of c and the sum of b.

x² + 7x + 10

The factors of ten are : 1 x 10, 2 x 5

2 and 5 have the sum of 7

Both terms are positive so the factor is then (x + 2)(x + 5)

If a is a number higher than 1, we can use methods such as guess and test.

5x² + 9x + 4

Since the sum of 5 and 4 is 9, we can guess that the factor is

(5x + 4)(x + 1)

Because we distributed, it equals 5x² + 9x + 4

 

Now, we can use what we know of factoring terms to solve a quadratic equation.

A quadratic equation looks like

s² – 2s – 35 = 0

There is an x² term, and it is equal to 0.

 

To solve this, we can factor one side. Since there is no common factors, we can skip difference of squares (since there is 3 terms, not 2) and factor the pattern the easy way. -7 and 5 have the sum of -2 and -35.

(s – 7)(s + 5) = 0

s – 7 = 0

+ 7

s = 7

s + 5 = 0

-5

s = -5

s equals 7 or -5