Question

Please help with algebra 2

Answer 1

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