Question

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

Answer 1

Answer:

The remainder is 80

Step-by-step 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

Answer 2

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