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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.

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sqdancefan

Answer:

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

Step-by-step 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 ...

  [tex](x^4-10x^3+3x^2+7x-47)\div(x+2)=\boxed{x^3-12x^2+27x-47+\dfrac{47}{x+2}}[/tex]

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