Answer:
- 8 or A
Step-by-step explanation:
Problem 1
First of all, you could write f(x) in terms of its x intercepts.
x = - 2
x + 2 = 0
x= 1
x - 1 = 0
x = 4
x - 4 = 0
So f(x) = (x - 4)(x - 1)(x + 2)
The division to find the remainder can be done expanding this further and doing a synthetic division on it, but the easier way is just to put 2 in for x. That is because x - 2 is turned into 0 by making x = 2
f(2) = (2 - 4)(2 - 1)(2 + 2)
f(2) = (-2)(1)(4)
f(2) = - 8
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The expanded form of this question is f(x) = x^3 - 3x^2 - 6x + 8
You could do this with synthetic division. It will give you the same answer.
2 || 1 -3 -6 8
2 -2 -16
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1 -1 -8 -8
The remainder is -8
Answer: A
which gives you exactly the same answer. (x - 2) into x^3 - x^2 - 16x + 16 will leave a remainder of - 12
Problem 2
