Question

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)

Answer 1

Answer: Question 4= C. (x + 2) Question 5= C. (x - 5)

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

A. (x - 2)

B. (x - 1)

C. (x + 2)

D. (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?

A. (x + 1)

B. (x + 4)

C. (x - 5)

D. (x - 2)

Explanation:

- For question number 4 the correct answer would be C. (x + 2)

- For question number 5 the correct answer would be C. (x - 5)

I just did the assignment and the answers above are correct. Hope this helps. Good Luck!!

Answer 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 )