Question

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

Answer 1

ANSWER

Quotient:

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

Remainder:

$r(x) = 11x - 29$

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

$r(x) = 11x - 29$