# Math Help - factor each of the following completely

1. ## factor each of the following completely

can somone help me with these 2 problems

1st problem 12x^3+28x^2-27x-63

2nd problem 216x^3+1000

if you could just show me step by step how its solved so i can figure out the other few i gota do and not use confusing math terms

2. Hints:

12x^3+28x^2-27x-63=4x^2(3x+7)-9(3x+7)

216x^3+1000=(6x)^3 + 10^3

3. I'm assuming the question is to solve these equations equal to zero?
For the first equation you have $12x^3+28x^2-27x-63=0$ yes?
You can factorise this into $(2x-3)(6x^2+23x+21)$ and then solve this either by factorising, or using the quadratic formula.

For the second, you have $216x^3-1000=0$ which you can reduce to $27x^3-125=0$ or $27x^3=125$. Then take the cube root of each side.
Hope this helps.

4. Originally Posted by worc3247
I'm assuming the question is to solve these equations equal to zero?
Why would you assume that? The post said "factor", why not factor?

For the first equation you have $12x^3+28x^2-27x-63=0$ yes?
You can factorise this into $(2x-3)(6x^2+23x+21)$ and then solve this either by factorising, or using the quadratic formula.

For the second, you have $216x^3-1000=0$ which you can reduce to $27x^3-125=0$ or $27x^3=125$. Then take the cube root of each side.
Hope this helps.
Actually, it was $216x^3+ 1000$ but it is still true that
$a^3+ b^3= (a+ b)(a^2- ab+ b^2)$