179k views
3 votes
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 .

User Jun Tian
by
8.3k points

1 Answer

5 votes
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
Determine the quotient, q(x), and remainder, r(x) when f(x) = 12x4 + 24x3 + 39x2 + 31x-example-1
User Hamid Shatu
by
7.8k points