Question

Show your process (best you can) for finding the remainder for the quotient:x%5E2%20%2B%2018x%20-%2012%20%29%20%C3%B7%20%28x-4%29" id="TexFormula1" title="(4x^3 - 20x^2 + 18x - 12 ) ÷ (x-4)" alt="(4x^3 - 20x^2 + 18x - 12 ) ÷ (x-4)" align="absmiddle" class="latex-formula">
(THAT A THING IS A divide SIGN)

Answer 1

Answer:

  -4

Step-by-step explanation:

The polynomial remainder theorem tells you the remainder from division by (x-4) is the dividend evaluated at x=4.

For f(x) = 4x³ -20x² +18x -12 = ((4x -20)x +18)x -12, we can find f(4) to be ...

  f(4) = ((4·4 -20)4 +18)4 -12 = (-4·4 +18)4 -12 = 2·4 -12

  f(4) = -4

The remainder from the division is -4.

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The above math is similar to the computation that would result from synthetic division. In synthetic division, the goal is to produce both the quotient and the remainder.