Factors and Remainders?

Question

I need help with this 5 part question that I have no idea how to solve.

Factors and Remainders
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1. When x^3 + a is divided by x + 2, the remainder is known to be -15. Find the numerical value of "a".

2. Find the value of "a" above when x + 2 is replaced by x - 2.

3. Find the smallest value of "a" for which x^3 + a is exactly divisible by x+2

4. If x - a is a factor of x^2 + 2ax - 3, find the numerical value(s) of "a".

5. Find the remainder when x^6 + 1 is divided by x - m.
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Please help me, with explanations of how to do each step. Math has always been my weakest subject, and if possible, can anyone at least point me in the direction, and I'll do the calculating?

Thanks a lot,

Matt

Also, I need help ASAP so I can turn this in a few hours. I'll greatly appreciate anyone's help.

I cannot ask the teacher because its a project.

Please help.... :\

Answer 1

start to divide! thats the hint, if you don't know why get a text book, but here are the answers for now:

1.
(x^3+a) | x+2
-------------------
-x^3-x^2 x^2-2x+4
-----------
-2x^2+a
2x^2+4x
-----------
4x+a
-4x-8
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-8+a (the remainder) = -15 ---> a=-7

2. the same procedure

3. set remainder=0 --> a=8

4. devide mate it gotta be a=-1 or a=1

5. ran outa patience

Answer 2

1.
. . . . x^2 - 2x + 4
x + 2)x^3 + . . . . . . . . . + a
. . . . x^3 + 2x^2
. . . . . . .. - 2x^2
. . . . . . .. - 2x^2 - 4x
. . . . . . . . . . . . .. 4x
. . . . . . . . . . . . . 4x + 8
. . . . . . . . . . . . . . . . - 8 + a = - 15

All the rest use the same approach. #2 and #3 can be solved by inference from #1.

Answer 3

please ask ur maths teacher