Basics on Factoring Quadratics

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Quadratic: ax² + bx + c = 0

When a = 1:

You find two numbers that add up to "b" which also multiply to equate to "c".

For example:

x² + 8x + 15 = 0

Factors of 15: 1, 15, 3, and 5.

You HAVE to find factors BEFORE you find addends! 

Which pair adds up to 8?

3 and 5

Therefore, your factored form will be: (x+3)(x+5) = 0

What happens when a doesn't equal 0? 

You still have to find two numbers that add up to "b", but also multiplies to equal to "ac".

For example: 

12x² - 13x + 3

ac: Multiply 12 and 3 = 36 

b: NEGATIVE 13 (signs matter!)

Factors of 36: 1, 36, 2, 18, 3, 12, 4, 9, 6, 6, 

 Hmm... I can't seem to find anything. Let me check the signs in the original equation.

If b is negative but c is positive...that means our two numbers HAVE to be negative. 

That's because adding negative numbers gives us a negative number (b).

But multiply two negative numbers gives us a POSITIVE number (c). 

So... I can just make any pair negative. I'm going to choose 9 and 4. Watch what happens!

NEGATIVE 9 + NEGATIVE 4 = NEGATIVE 13.

That will be my pair! -9 and -4!

Therefore, my factored form is: (x - 9)(x - 4) = 0

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