Question

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

Answer 1

ANSWER

Quotient:

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

Remainder:

$r(x) = 2x + 6$

EXPLANATION

The given functions are

$f(x) = 12 {x}^{4} + 20 {x}^{3} + 40 {x}^{2} + 30x + 25$

and

$g(x) = 3 {x}^{2} + 2x + 5$

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

We perform the long division as shown in the attachment.

The quotient is

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

and the remainder is

$r(x) = 2x + 6$