Question

Find the remainder when f(x) is divided by (x - k).

f(x) = 8x4 + 7x3 + 5x2 - 5x + 35; k = 4

Answer 1

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

Answer 2

the remainder is equal to
`2,591`

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`