Question

Find the remainder when f(x) is divided by (x - k). f(x) = 8x4 + 7x3 + 5x2 - 5x + 35; k = 4

Answer 1

Answer:

the remainder is equal to $2,591$

Step-by-step explanation:

we know that

The remainder theorem, states that if f(x) is a polynomial in x then the remainder on dividing f(x) by  (x − k) is equal to f(k)

In this problem we have

$f(x)=8x^{4}+7x^{3}+5x^{2} -5x+35$

the value of k is equal to $k=4$

Find f(k)

$f(4)=8(4)^{4}+7(4)^{3}+5(4)^{2} -5(4)+35$

$f(4)=2,591$

therefore

the remainder is equal to $2,591$

Answer 2

Using the remainder theorem, evaluating the function for k will be the same value as the remainder.
8(4^4) + 7(4^3) + 5(4^2) -5(4) + 35 =
2048 + 448 + 80 + - 20 + 35 =
2591