Question

How do you factor `8x^3+4x^2-18x-9`?

Answer 1

`8x^3+4x^2-18x-9=(2x-3)(2x+3)(2x+1)`

Explanation:

Notice that the ratio between the first and second terms is the same as that between the third and fourth terms. So we can factor this cubic by grouping:

`8x^3+4x^2-18x-9`

`=(8x^3+4x^2)-(18x+9)`

`=4x^2(2x+1)-9(2x+1)`

`=(4x^2-9)(2x+1)`

`=((2x)^2-3^2)(2x+1)`

`=(2x-3)(2x+3)(2x+1)`

Note that we also used the difference of squares identity:

`a^2-b^2=(a-b)(a+b)`

with `a=2x` and `b=3`