Use the Remainder Theorem to find the remainder when f(x) = x^4 + 4x^3 - x^2 - 16x -12 is divided by x - 4.
1 answer:
Answer:
420
Step-by-step explanation:
The remainder theorem tells you the remainder is f(4), which you can find by evaluating the expression for x=4. Evaluation is simpler if the expression is written in Horner form first.
... f(x) = (((x +4)x -1)x -16)x -12
... f(4) = (((4 +4)4 -1)4 -16)4 -12
... = ((8·4 -1)4 -16)4 -12
... = (31·4 -16)4 -12
... = 108·4 -12 = 420
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<em>Comment on evauation using Horner's form</em>
The intermediate results (contents of parentheses) are the same as the intermediate results you get when you use synthetic division.
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