Question

Factor completely x3 + 3x2 − 6x − 18.

Answer 1

You can factor this by using the grouping method.

$(x^3+3x^2)-(6x+18)$

$x^2(x+3)-6(x+3)$

Since both groups have the (x+3), that is one of the factors of the polynomial. What is remaining (the x^2 and -6), is the other factor.

Here are the factors:

$(x^2-6)(x+3)$

Neither can be simplified further, so this is your answer. Hope this helps!

Answer 2

$x^3+3x^2-6x-18=x^2(x+3)-6(x+3)=(x+3)(x^2-6)\\\\=(x+3)(x^2-(\sqrt6)^2)=(x+3)(x-\sqrt6)(x+\sqrt6)\\\\Used:\\\\a^2-b^2=(a-b)(a+b)$