Question

Use synthetic division to find the result when x4−10x3+3x2+7x−47 is divided by x+2.

Write your answer in the form q(x)+r(x)d(x), where q(x) is the quotient, r(x) is the remainder, and d(x) is the divisor.

Answer 1

p(x) = x^3 -12x^2 +27x -47 +47/(x+2)

Explanation:

The synthetic division is shown and explained in the attachment.

The quotient is ...

q(x) = x^3 -12x^2 +27x -47

The remainder is ...

r(x) = 47

Then the division can be written as ...

`(x^4-10x^3+3x^2+7x-47)/(x+2)=\boxed{x^3-12x^2+27x-47+(47)/(x+2)}`