Question

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

Answer 1

ANSWER

Quotient:

$q(x) = 4 {x}^{2} + 3x + 2$

Remainder:

$r(x) = 3x + 1$

EXPLANATION

The given functions are

$f(x) = 12 {x}^{4} + 21 {x}^{3} + 31 {x}^{2} + 21x + 9$

and

$g(x) = 3 {x}^{2} + 3x + 4$

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

We perform the long division as shown in the attachment.

The quotient is

$q(x) = 4 {x}^{2} + 3x + 2$

The remainder is

$r(x) = 3x + 1$