ANSWER
Quotient:
[tex]q(x) = 4{x}^{2} + 4x + 5[/tex]
Remainder:
[tex]r(x) = 4x + 1[/tex]
EXPLANATION
The given functions are:
[tex]f(x) = 8 {x}^{4} + 16 {x}^{3} + 26 {x}^{2} + 22x + 11[/tex]
and
[tex]g(x) = 2 {x}^{2} + 2x + 2[/tex]
We want to find the quotient and remainder when f(x) is divided by g(x).
We carry out the long division as shown in the attachment .
The quotient is
[tex]q(x) = 4{x}^{2} + 4x + 5[/tex]
and the remainder is
[tex]r(x) = 4x + 1[/tex]
