Question

Divide (long division)

(4n^4+4n^3+16n^2)+4^2

Answer 1

9514 1404 393

Answer:

  n^2 +n +4

Step-by-step explanation:

Since the divisor has only one term, the quotient is formed by dividing the terms one at a time.

  $\dfrac{4n^4+4n^3+16n^2}{4n^2}=\dfrac{4n^4}{4n^2}+\dfrac{4n^3}{4n^2}+\dfrac{16n^2}{4n^2}=\boxed{n^2 +n +4}$

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Your long division tableau will subtract n^2×4n^2 = 4n^4 to form the new dividend 4n^3+16n^2. Then you will subtract n×4n^2 = 4n^3 to get the new dividend of 16n^2. The final quotient term is 4, and you will subtract 4×4n^2 to get a remainder of 0. You will have written the quotient as n^2+n+4.