Question

I need help with factoring polynomials by grouping. Here's an example. 3n^3 – 6n^2 + 4n – 8

Answer 1

Find the GCF of the first two terms and factor it out.
Find the GCF of the last two terms and factor it out.

Answer 2

When finding the GCF of 3n^3 – 12n^2, my book says the answer is 3n^2(n – 4). I understand the 3n^2, but where does the (n - 4) come from?

Answer 3

Factoring is the opposite of multiplying out.
Look at this simple example.
Factor x^2 - x. The GCF is x, so an x comes out.
x( )
Now you need to put inside the parentheses the quantities that when multiplied by x will give you back x^2 - x.
x( ) = x^2 - x
What times the x outside will give you x^2? An x, so an x goes inside the parentheses:
x(x ) = x^2 - x
Now what times the x outside will give you -x? -1, so the -1 goes inside the parentheses.
x(x - 1) = x^2 - x
Check: multiply x(x - 1) by distributing the x: x^2 - x, so factoring is correct.

Answer 4

Now let's look at your problem.
The first two terms are 3n^3 - 6n^2, and you understand the GCF is 3n^2.
The factorization is going to end up as:
3n^2( )
What do you need to multiply 3n^2 by to get 3n^3? Answer: n
3n^2(n )
What do you need to multiply 3n^2 by to get -6n^2? Answer: -2
3n^2(n - 2)

Answer 5

Your question:
When finding the GCF of 3n^3 – 12n^2, my book says the answer is 3n^2(n – 4). I understand the 3n^2, but where does the (n - 4) come from?

See above answer. It's similar.
3n^3 - 12n = 3n^2( )
3n^2 times what equals 3n^3? Answer: n, so
3n^3 - 12n = 3n^2(n )
3n^2 times what equals -12n? Answer: -4, so
3n^3 - 12n = 3n^2(n - 4)

Answer 6

Thank you. My mathbook showed the answers to the example problem but for some reason didn't really show how to get the answers. I understand it now.

Answer 7

Here's the rest of the factorization:
3n^3 – 6n^2 + 4n – 8
3n^2(n - 2) +4(n - 2)
(n - 2)(3n^2 + 4)