Show your process (best you can) for finding the remainder for the quotient:(4x^3 - 20x^2 + 18x - 12 ) ÷ (x-4) (THAT A THING IS A divide SIGN)

Question

Show your process (best you can) for finding the remainder for the quotient:
`(4x^3 - 20x^2 + 18x - 12 ) ÷ (x-4)`

(THAT A THING IS A divide SIGN)

Answer 1

-4

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.