Question

Factor –8x3 – 2x2 – 12x – 3 by grouping. What is the resulting expression?

Answer 1

Answer: $(4x+1)(-2x^2-3)$

Step-by-step explanation:

To factor the given polynomial $-8x^3-2x^2-12x-3$

First group the first two terms and the last two terms together respectively.

i.e. $(-8x^3-2x^2)+(-12x-3)$

Take out GCF from each binomial, we get

$-2x^2(4x+1)-3(4x+1)$

Now, factor out the common binomial, we get the resulting expression as

$=(4x+1)(-2x^2-3)$

Answer 2

Easier if you first factor out the " - " sign.  Then you have:

–8x3 – 2x2 – 12x – 3    = -1(8x3 + 2x2 + 12x +3).

Start with 12 + 3.  This factors to 3(4x+1).  Next, focus on 8x^3+2x^2.  This factors to 2x^2*(4x+1).  So, the binomial factor 4x+1 is common to the first two terms and the second two terms.  We get:  (4x+1) (  2x^2  + 3).

Now put the "-" sign back in, and we get   - (4x+1) ( 2x^2  + 3)    (answer)

Please note:  Use "^" to denote exponentiation.   2x2 is meaningless; it should be 2x^2.