Question

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

f(x) = 4x4 + 12x3 + 17x2 + 19x + 6

is divided by g(x) = 4x2 + 4x + 5 .

Answer 1

ANSWER

Quotient:


`image`

Remainder:


`r(x) = 11x - 29`

Step-by-step explanation

The given functions are


`f(x) = 4 {x}^(4) + 12 {x}^(3) + 17 {x}^(2) + 19x + 6`

and


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

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

We perform the long division as shown in the attachment.

The quotient is


`q(x) = {x}^(2) - 4x + 7`

The remainder is


`r(x) = 11x - 29`