How do I factor expression

Question

please help me completely factor this expression.

 

       4x^2 - 8x - 12 + 6x

 

 

 

thanks!

Answer 1

4x^2 - 8x - 12 + 6x.

-8x+6x = -2x, so original expression is equivalent to:
4x^2 - 2x - 12

Change each term to a product of prime factors:
2*2*x*x - 2*x - 2*2*3

Factor out the Greatest Common Factor = 2 using distributive property:
2*(2*x*x - x - 2*3)

Assume factors like this:
2*(2x+a)*(x+b) = 2*(2xx + (a+2b)x + ab)

Then a+2b = -1 and ab = -2*3.
So we’re looking for factors, a and b, of -2*3 = -6
such that a+2b = -1.

 

.a … b … a+2b
-1 … 6 … 11
-2 … 3 … 4
-3 … 2 … 1
.3 … -2 … -1 <== this one.

So 2*(2x+3)*(x-2) is the answer.

Check:
2*(2x+3)*(x-2) =? 4x^2 - 8x - 12 + 6x
2*(2xx-2*2x+3x-2*3) =? 4x^2 - 8x - 12 + 6x
2*2xx-2*2*2x+2*3x-2*2*3 =? 4x^2 - 8x - 12 + 6x
4x^2-8x+6x-12 = 4x^2 - 8x - 12 + 6x √

Answer 2

First combine like terms to get 4x²-2x-12

factor out a 2, since it's a common factor for each term

2(2x²-x-6)

Now factor the polynomial using any factoring method you've learned to get

2(2x+3)(x-2)