what is the remainder when the function

Question

f(x)=x^4-3x^3+7x-1 is divided by (x-2)

A. 2
B. 5
C. 17
D. 25

Use the factor theorem to determine if (x-4) is a factor of x^5-3x^4-x-3
A. (x-4) is a factor because f(4)=0
B. (x-4) is a factor because f(4)≠0
C. (x-4) is not a factor because f(4)=0
D. (x-4) is not a factor because f(4)≠0

Answer 1

To find the remainder when f(x) = x^4 - 3x^3 + 7x - 1 is divided by (x-2), we can use synthetic division.

We set up the division with 2 as the divisor:

2 | 1 -3 7 -1
-----------------------
2 -2 10 19

The remainder is the last value in the bottom row, which is 19.

Therefore, the remainder when f(x) is divided by (x-2) is 19.

To determine if (x-4) is a factor of f(x) = x^5 - 3x^4 - x - 3, we can use the factor theorem.

The factor theorem states that if (x-a) is a factor of f(x), then f(a) = 0.

To use this theorem, we substitute the value of a = 4 into f(x) and check if f(4) = 0.

f(4) = (4)^5 - 3(4)^4 - (4) - 3
= 1024 - 3(256) - 4 - 3
= 1024 - 768 - 7
= 249

Since f(4) is not equal to 0, (x-4) is not a factor of f(x).

Therefore, the answer is D. (x-4) is not a factor because f(4)≠0.