Factoring Quadratic Equations

Simply put, a quadratic is nothing but a polynomial that looks like “ax2 + bx +c” where all a, b and c are a number, but the important thing is either b and c can be 0, but can never be a zero. A quadratic equation can be easily solved, applying algebra rules along with applying all the factoring methods. In other words, we call it factoring, only because we are finding the factors of the quadratic equation.
Let’s explain this concept, if factoring quadratic equations, with a simple example:

X2 + 3x -4

This is a simple quadratic equation. If factoring a quadratic equation is all about finding factors, then we need to determine the factors, or a factor, that that we multiply by.
So, the factors of X2 + 3x -4 are:

(x+4) (x-1)

Because when you multiply these factors you get:

(x+4) (x-1) = x2 -x + 4x -4 = X2 + 3x -4

Remember expanding an equation and factoring are totally different – where expanding is quite simple, factoring is difficult – it’s as if you want to find the ingredients of a tasty pizza after it was delivered. Yes, only the chef could tell you that!. In the same way, factoring can be difficult unless you know the concept behind it.

Example: 1 – Factor x^2 + 5x + 6

Find 2 numbers that added together get to 5 and then multiply to get 6.

2 and 3 will work:

2 + 3 = 5
2 * 3 = 6
x^2 + 5x + 6 = (x+2) (x+3)

Example: 2 – Factor 8X2 – 2x = 0

In this case, find the greatest common factor of both terms:

8x^2: 1, 2, 4, 8, x, x
2x: 1, 2, x

The GCF is 2x, so factor a 2x fr0m the expression:

2x (4x – 1) = 0

Example 3 – Factor 3x^2 + 10x + 8

a*c = 3 * -8 = -24
b = 10

Find two numbers that multiply to get -24 and then add to get to 10.

4 and 6 will work.

4 * 6 = 24
4 + 6 = 10
3x^2 + 4x + 6x + 8

group the first 2 and last 2 terms:

(3x^2 + 4x) + (6x +8)

factor each grouped term:

x(3x+4) + 2(3x+4)
(3x+4) (x+2)