Given the binomials (x - 2), (x - 1), (x + 2), and (x - 4), which one is a factor of f (x) = x3 + 7x2 + 14x + 8?

(x - 2)

(x - 1)

(x + 2)

(x - 4)

Given the binomials (x + 1), (x + 4), (x - 5), and (x - 2), which one is a factor of f (x) = 3x3 - 12x2 - 4x - 55?

(x + 1)

(x + 4)

(x - 5)

(x - 2)

We will use the Reminder theorem.

The polynomial f (x) is divisible by x - a when f (a) = 0.

For the 1st one:

f ( - 2) = ( - 2) ³ + 7 · ( - 2) ² + 14 · ( - 2) + 8 =

= - 8 + 28 - 28 + 8 = 0

For the 2nd one:

f (5) = 3 · 5³ - 12 · 5² - 4 · 5 - 55 =

= 375 - 300 - 20 - 55 = 375 - 375 = 0

Answer;

1. (x + 2)

2. (x - 5)