Question

Find the remainder when f(x) is divided by (x - k).
f(x) = 4x3 - 5x2 + 2x + 11; k= 3

Answer 1

3] 4 -5 2 11
12 21 69
----------------------
4 7 23 80

80 would be the remainder
Another method would be to plug 3 into the equation for x

`4(3)^(3)-5(3)^(2)+2(3)+11` = 4(27) - 5(9) + 6 + 11 = 108 - 45 + 6 + 11 = 63 + 6 + 11 = 80

Answer 2

The remainder is 80

Explanation:

Given the polynomial

`f(x)=4x^3-5x^2+2x+11`

we have to find the remainder when the above polynomial f(x) is divided by x-3

By remainder theorem when we put x=3 in f(x) we get the remainder i.e f(3)

`f(3)=4(3)^3-5(3)^2+2(3)+11`

`=108-45+6+11`

`=80`

which is required remainder.

Hence, the remainder is 80