Answer:
B, E
Step-by-step explanation:
It can be helpful to factor the first two terms:
f(x) = x^2(x -7) +36
This can make it easier to evaluate the function for different values of x.
The answer choices suggest you need to know whether f(5) and f(-14) match the values given here.
f(5) = 5^2(5 -7) +36 = -50 +36 = -14 . . . . matches choice B (and E)
f(-14) = (-14)^2(-14-7) +36 = -21(196) +36 . . . . <em>does not match</em> choice A (or D)
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The one remaining answer choice we need to consider is C. If we look at f(0) for this equation, we find it is (-5)(-10) +14 = 64, which <em>does not match</em> f(0) = 36 for the function given in the problem statement.
The only true answer choices are B and E.
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The remainder theorem tells you that f(a) = the remainder from f(x)/(x -a).
