Question

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

f(x) = 12x4 + 24x3 + 39x2 + 31x + 21

is divided by g(x) = 6x2 + 3x + 6 .

Answer 1

ANSWER

Quotient:


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

Remainder:


`r(x) = 4x + 3`

Step-by-step explanation

The given functions are:


`f(x) = 12 {x}^(4) + 24 {x}^(3) + 39 {x }^(2) + 31x + 21`

and


`g(x) = 6 {x}^(2) + 3x + 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) = 2 {x}^(2) + 3x + 3`

and the remainder is


`r(x) = 4x + 3`