Question

If f(x) = x3 + 5, then what is the remainder when f(x) is divided by x + 3?

Answer 1

Answer: -22

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Explanation:

You could use synthetic division or polynomial long division to find the answer, but a much quicker way is to apply the remainder theorem.

That theorem says that if we divide p(x) over (x-k), then the remainder is p(k).

We're dividing over x+3, or x-(-3), so we can see that k = -3 in this case.

Plug this into the function

f(x) = x^3+5

f(-3) = (-3)^3 + 5

f(-3) = -27 + 5

f(-3) = -22 is the remainder

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If you want to use polynomial long division or synthetic division, then check out the diagram below.