Question

p(x)=x^3+2x^2-4x-8 how do you factor this polynomial function

Answer 1

Steps:

So for this, I will be factoring by grouping. Firstly, factor x³ + 2x² and -4x - 8 separately. Make sure that they have the same quantity inside of the parentheses:

$p(x)=x^2(x+2)-4(x+2)$

Now we can rewrite it as:

$p(x)=(x^2-4)(x+2)$

However, we aren't finished factoring yet. The first factor, x² - 4, can be factored further using the difference of squares. The difference of squares goes by the formula here: $x^2-y^2=(x+y)(x-y)$ . In this case:

$x^2-4=(x+2)(x-2)\\p(x)=(x+2)(x-2)(x+2)$

Answer:

In short, the answer is $p(x)=(x+2)(x-2)(x+2)\ \textsf{OR}\ p(x)=(x-2)(x+2)^2$