# 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)#

Select one:

a.

b.

c.

d.

##### 1 Answer

#### Answer:

b.

#### Explanation:

Note that the coefficient of **a** and **c** immediately.

Looking at the coefficient of **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#

**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^3+2x^2-15x = x(x^2+2x-15)#

Next look for a pair of factors of

The pair

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

Putting it all together we have:

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