SOLUTION: p(x)=3x^3+ax-2 In the function above, a is a constant.If the remainder when P(x) is divided by x +1 is 2, what is the value of a? A) -7 B) -5 C) 5 D) 7

Algebra ->  Expressions -> SOLUTION: p(x)=3x^3+ax-2 In the function above, a is a constant.If the remainder when P(x) is divided by x +1 is 2, what is the value of a? A) -7 B) -5 C) 5 D) 7      Log On


   

Question 1043537: p(x)=3x^3+ax-2
In the function above, a is a constant.If the remainder when P(x) is divided by x +1 is 2, what is the value of a?
A) -7
B) -5
C) 5
D) 7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x+1 is equivalent to x-(-1)


x-(-1) is in the form x-k where k = -1


So we'll plug x = -1 into P(x) to get


P%28x%29+=+3x%5E3%2Ba%2Ax-2


P%28-1%29+=+3%28-1%29%5E3%2Ba%2A%28-1%29-2 Replace every x with -1


P%28-1%29+=+3%28-1%29%2Ba%2A%28-1%29-2


P%28-1%29+=+-3-a-2


P%28-1%29+=+-a-3-2


P%28-1%29+=+-a-5


Now replace P(-1) with 2. Why 2? Because this is the remainder. I'm using the remainder theorem.


P%28-1%29+=+-a-5


2+=+-a-5 Replace P(-1) with 2


Now we solve for 'a'


2+=+-a-5


2%2Ba+=+-a-5%2Ba Add 'a' to both sides


2%2Ba+=+-5


a%2B2+=+-5


a%2B2-2+=+-5-2 Subtract 2 from both sides


a+=+-7


So the final answer is choice A) -7