Question

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

f(x) = 12x4 + 21x3 + 31x2 + 21x + 9

is divided by g(x) = 3x2 + 3x + 4 .

Answer 1

ANSWER

Quotient:


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

Remainder:


`r(x) = 3x + 1`

Step-by-step 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`