Question

Write the polynomial in factored form? `x^3 + 2x^2 - 15x`

Select one:
a. `-3x(x + 5)(x + 1)`
b. `x(x - 3)(x + 5)`
c. `5x(x + 1)(x - 3)`
d. `x(x + 5)(x + 3)`

Answer 1

b. `x(x-3)(x+5)`

Explanation:

Note that the coefficient of `x^3` is `1`, so we can eliminate a and c immediately.

Looking at the coefficient of `x`, which is negative, we can also rule out d, which is all positive.

So the only possibility is b.

Does it work?

`x(x-3)(x+5) = x(x^2+(5-3)x+(-3)(5))`

`color(white)(x(x-3)(x+5)) = x(x^2+2x-15)`

`color(white)(x(x-3)(x+5)) = x^3+2x^2-15x`

`color(white)()`
Footnote

If we were factoring this without the multiple choice answers, then we could proceed as follows:

Given:

`x^3+2x^2-15x`

First note that all of the terms are divisible by `x`, so we can separate that out as a factor:

`x^3+2x^2-15x = x(x^2+2x-15)`

Next look for a pair of factors of `15` which differ by `2`.

The pair `5, 3` works, so we find:

`x^2+2x-15 = (x+5)(x-3)`

Putting it all together we have:

`x^3+2x^2-15x = x(x+5)(x-3)`