How do you factor #2x^3 + 2x^2 - 84x#?

2 Answers
Aug 13, 2016

Answer:

#2x(x+7)(x-6)#

Explanation:

The first step is to take out the #color(blue)"common factor"# of 2x

#rArr2x(x^2+x-42) ........ (A)#

Now factorise the #color(blue)"quadratic"# inside the bracket.

Using the a-c method, find the factors of - 42 which sum to +1

These are +7 and - 6

#rArrx^2+x-42=(x+7)(x-6)#

substituting these into (A) gives the factorised form.

#rArr2x^3+2x^2-84x=2x(x+7)(x-6)#

Aug 13, 2016

Answer:

#2x(x^2+x-42)=2x(x-6)(x+7)#

Explanation:

And from this start:

#x^2+x-42=(x-6)(x+7)# (If this were not immediately obvious, I could have used the quadratic equation and solved for #x# in the quadratic.

And thus, #2x^3+2x^2-84x# #=# #2x(x-6)(x+7)#