calculate the value of a when 3ax^3+2x^2-7x+3 divided by 2x+1. gives a remainder of( -a over 2)

Question

3ax³+2x²-7x+3  divided by 2x+1 gives a remainder of  (-a/2)

Answer 1

Let's take a regular division problem first. 100/21 = 4 R 16 which if you checked you would do 4*21 +16 which is 100.

21 is the divisor, 4 is the quotient, 16 is the remainder.

 

P(x) = (divisor)*q(x) + r(x) is how this looks for polynomials. P(x) is the original, q(x) is the quotient, and r(x) is the remainder.

 

For your example:

P(x) = (2x +1)*q(x) + r(x) if you plug in x = -1/2 you get

P(-1/2) = 0*q(-1/2) + r(-1/2)

P(-1/2) = r(-1/2) so plug -1/2 into these 2 expressions to get

 

-3a/8  + 1/2 + 7/2 +3 =  -a/2

-3a/8  + 7                    = -a/2 

             7                      = -a/8

                       -56        = a

 

This means that when -168x^3 + 2x^2 - 7x + 3 is divided by 2x + 1, the remainder is 56/2 or 28.

 

Just performed the actual long division and got the remainder of 28.....so this is right.

Hope this helped.