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

Question

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

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Answer 1 · 2017-03-03T22:19:07

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

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:

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