SOLUTION: When x^5+px^3+2x^2-6x-8 is divided by (x+2) the remainder is 4. Find P. I used synthetic divison; identified that p-40=4 (4 being the remainder and p-40 being the quotient) p

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Question 935165: When x^5+px^3+2x^2-6x-8 is divided by (x+2) the remainder is 4. Find P.
I used synthetic divison; identified that p-40=4 (4 being the remainder and p-40 being the quotient)
p=44
However, I am told that p=-3

Found 2 solutions by Theo, MathLover1:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
that's correct.
p = -3.

you need to include 0x^4 in the expression because you have to consider all the degrees of exponents from the highest down to the constant.

your expression becomes:

x^5 + 0x^4 + px^3 + 2x^2 - 6x - 8

you will be doing synthetic division by -2.

i did it vertically instead of horizontally so you can see each of the calculations easier.

your multiplier is -2.

your multiplicand is:

1 for x^5
0 for 0x^4
p for px^3
2 fpr 2x^2
-6 for -6x
-8 for -8

applying the synthetic division algorithm, we get:

1 = 1
0 - 2 * 1 = -2
p - 2 * (-2) = p + 4
2 - 2 * (p + 4) = 2 - 2p - 8 = -2p - 6
-6 - 2 * (-2p - 6) = -6 + 4p + 12 = 4p + 6
-8 - 2 * (4p + 6) = -8 - 8p - 12 = -8p - 20

you now set -8p - 20 equal to 4 and solve for p as follows:
-8p - 20 = 4
add 20 to both sides of the equation to get -8p = 24
divide both sides of the equation by -8 to get p = -3

that's your solution.

Answer by MathLover1(20850) (Show Source):
You can put this solution on YOUR website!

Then substitute the value of from to the given equation above.

Then solve for