Question

10: Find the remainder of the division problem shown below.
(x^4 + x^3 – 3x – 3) ÷ (x-2)
Answer:________

12: Is the term (x+2) a factor of the polynomial shown below?
f(x) = x^3 – 10x^2 + 27x – 12

A: Yes, the remainder is 0.
B: Yes, the remainder is -114.
C: No, but the remainder is 0.
D: No, but the remainder is -114.

Answer 1

Answer on Question #56625–Math -Algebra

1. Find the remainder of the division problem shown below.

$$(x^4 + x^3 - 3x - 3) \div (x - 2)$$

Solution

$$f(x) = x^4 + x^3 - 3x - 3$$ $$f(2) = 2^4 + 2^3 - 3 \cdot 2 - 3 = 16 + 8 - 6 - 3 = 15.$$

Answer: 15.

2. Is the term $(x + 2)$ a factor of the polynomial shown below?

$$f(x) = x^3 - 10x^2 + 27x - 12$$

A. Yes, the remainder is 0.

B. Yes, the remainder is -114.

C. No, but the remainder is 0.

D. No, but the remainder is -114.

Solution

If the term $(x + 2)$ is a factor of the $f(x)$ the remainder is 0. So, B. and C. are wrong answers. Now find the remainder:

$$f(-2) = (-2)^3 - 10 \cdot (-2)^2 + 27 \cdot (-2) - 12 = -8 - 40 - 54 - 12 = -114$$

Answer: D. No, but the remainder is -114.

www.AssignmentExpert.com