Question

Use the Remainder Theorem to find the remainder when f(x) = x^4 + 4x^3 - x^2 - 16x -12 is divided by x - 4.

36
420
548
-92

Answer 1

420

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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Comment on evauation using Horner's form

The intermediate results (contents of parentheses) are the same as the intermediate results you get when you use synthetic division.