Question

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

f(x) = 12x4 + 20x3 + 40x2 + 30x + 26

is divided by g(x) = 3x2 + 2x + 5 .

Answer 1

Quotient:

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

Remainder:

`r(x) = 2x + 6`

Step-by-step 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`