Ira S. answered • 09/18/14

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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.

Ira S.

Not a problem, glad I could help.

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09/22/14

Nobuhle G.

09/22/14