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)#