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.
