need some help solving it

Question

Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x),

and express the quotient P(x)/D(x) in the form P(x)D(x)= Q(x) + R(x)D(x)

.P(x) = x3 + 9x + 8, D(x) = x − 7

Answer 1

7 ) 1 0 9 8 All powers must be represented. The 0 is for the missing x² term.

Bring down the 1

7 ) 1 0 9 8

________

1 Multiply 7 times 1, place answer under the 0. Add down.

7 ) 1 0 9 8

__7______

1 7 Multiply 7 times 7, place answer under the o. Add down.

7 ) 1 0 9 8

__ 7_49_406___

1 7 58 414 Multiply 58 times 7, place answer under the 8. Add down. 414 is the remainder.

P(x) / Q(x) = x² + 7x + 58 + (414/(x-7)).

Answer 2

Q(x) = x² + 7x + 58

R(x) = 414/(x-7)

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