Question

Use the remainder theorem to factor

x^3 - 3x^2 - 13x + 15.

Select the appropriate response:

A) (x2 + 2x - 3)(x - 5)
B) (x2 + 2x - 4)(x - 5)
C) (x2 + 2x - 3)(x - 2)

Answer 1

A) (x2 + 2x - 3)(x - 5)

Explanation:

x³ - 3x² - 13x + 15

x = 5

5³ - 3(5)² - 13(5) + 15 = 0

So 5 is a root and x-5 is a factor

Since the constant is 15, it has to be

A) (x2 + 2x - 3)(x - 5)

(-5) × (-3) = 15

Answer 2

A is the correct choice

Explanation:

Use synthetic division to check:

x^3-3x^2-13x+15 / x-5

5 | 1 -3 -13 15

5 10 -15

_________

1 2 -3 0

This means x^2+2x-3 with no remainder which means A works