Question

Determine the quotient, q(x), and remainder, r(x) when

f(x) = 8x4 + 16x3 + 26x2 + 22x + 11

is divided by g(x) = 2x2 + 2x + 2 .

Answer 1

Quotient:

`q(x) = 4{x}^(2) + 4x + 5`

Remainder:

`r(x) = 4x + 1`

Step-by-step explanation

The given functions are:

`f(x) = 8 {x}^(4) + 16 {x}^(3) + 26 {x}^(2) + 22x + 11`

and

`g(x) = 2 {x}^(2) + 2x + 2`

We want to find the quotient and remainder when f(x) is divided by g(x).

We carry out the long division as shown in the attachment .

The quotient is

`q(x) = 4{x}^(2) + 4x + 5`

and the remainder is

`r(x) = 4x + 1`