Question

One of the factors of the polynomial x3 − 5x2 is x + 3. What is the other factor?

Answer 1

C. x² − 8x + 24 − 72/(x+3)

Explanation:

See attached picture for long division method.

Logically, we know x³ − 5x² factors to x² (x − 5). Since x + 3 isn't a factor, we know the remainder isn't 0. So we can narrow the options down to A or C.

One way to find the remainder is through long division. Or, since this is multiple choice, we multiply the options by x + 3 and see which one results in an answer of x³ − 5x².

(x + 3) (x² − 8x + 24 − 72/(x+3))

(x + 3) (x² − 8x + 24) − 72

x³ − 8x² + 24x + 3x² − 24x + 72 − 72

x³ − 5x²