Question

(x 4 - 81) (x - 3) . write answers in descending power of x. (division)

Answer 1

Answer:

  x^3+3x^2+9x+27

Step-by-step explanation:

$\dfrac{x^4-81}{x-3}=\dfrac{(x^2-9)(x^2+9)}{x-3}=\dfrac{(x-3)(x+3)(x^2+9)}{(x-3)}\\\\=(x+3)(x^2+9)=x^3+3x^2+9x+27$

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The factoring of the difference of squares is used (twice):

  a² -b² = (a -b)(a +b)