could someone help me factor this?

Question

Factor the following polynomials by grouping the terms together two at a time.

4x^3+6x^2-2x-3

 

so i tried it myself, ad got 2x(2x^2+3x) -(x-3) 

 

but i don't know what to do from here could someone please help

Answer 1

Hi Jay,

 

4x³ + 6x² - 2x -3

 

First, look for any GCF (Greatest Common Factors) (from each) before you start.  Always!!! because after taking the GCF out, it will be much easier to deal with when numbers/coefficients become smaller.

 

As you can see not all have something in common.  So, there is no "GCF: Greatest Common Factor" to take out from each term (to start with).

 

From first 2 terms (4x³ + 6x²), you can take out 2 (since both numbers are even) and x² for x's.

So, you take out 2x² from each term and you will come up with 2x² (2x + 3) for first two terms: (4x³ + 6x²).

 

From final 2 terms (-2x - 3), you can take out -1 (since both have - sign).

So, you take out -1 from each term and you will come up with - (2x + 3) for final two terms: (-2x - 3).

Remember, - (2x + 3) is same as -1 (2x + 3).

 

As you put this together, you will write 2x² (2x + 3) - (2x + 3).  From here, you will take out GCF again and it will be (2x + 3).  As you do that, you will be left with (2x² - 1) and (2x + 3).

 

To write original equation (Standard or General Form) to factored form, yours will be:

4x³ + 6x² - 2x - 3 = (2x² - 1) (2x + 3)

 

 

(2x² - 1) (2x + 3)  -->   (2x² - 1) (2x) = 4x³ - 2x    (2x² - 1) (3) = 6x² -3

Write the highest power first:  4x³ +6x² -2x -3

 

I hope you understood this.

 

Good luck to you.

 

 

If you want to take out 2x from first 3 terms, then yours will look like this:

 

2x (2x2 + 3x -1) -3.  And it will not look like FACTORED form: (x + y) (a + b) -> (2 binomial terms).