Question

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

Answer 1

ANSWER

Quotient:

$q(x) = 3 {x}^{2} + 4x + 1$

Remainder:

$r(x) = 4x + 2$

EXPLANATION

The given function is:

$f(x) = 12 {x}^{4} + 2 {x}^{3} + 30 {x}^{2} + 28x + 8$

and

$g(x) =4 {x}^{2} + 2x + 6$

We want to determine 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

$q(x) = 3 {x}^{2} + 4x + 1$

and the remainder is

$r(x) = 4x + 2$