melissalynne12 melissalynne12
  • 22-04-2019
  • Mathematics
contestada

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

f(x) = 4x4 + 12x3 + 17x2 + 19x + 6

is divided by g(x) = 4x2 + 4x + 5 .

Respuesta :

kudzordzifrancis
kudzordzifrancis kudzordzifrancis
  • 22-04-2019
ANSWER

Quotient:

[tex]q(x) = {x}^{2} - 4x + 7

[/tex]

Remainder:

[tex]r(x) = 11x - 29[/tex]

EXPLANATION

The given functions are

[tex]f(x) = 4 {x}^{4} + 12 {x}^{3} + 17 {x}^{2} + 19x + 6[/tex]

and

[tex]g(x) = 4 {x}^{2} + 4x + 5[/tex]

We want to find 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

[tex]q(x) = {x}^{2} - 4x + 7[/tex]

The remainder is

[tex]r(x) = 11x - 29[/tex]
Ver imagen kudzordzifrancis
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