SOLUTION: When the polynomial 2x^3+5x^2+mx+n is divided by 2x+1 where m and n are constants ,the quotient is x^2+2x+1 and the remainder is -8 .Find the value of m and n.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: When the polynomial 2x^3+5x^2+mx+n is divided by 2x+1 where m and n are constants ,the quotient is x^2+2x+1 and the remainder is -8 .Find the value of m and n.       Log On


   

Question 1200413: When the polynomial 2x^3+5x^2+mx+n is divided by 2x+1 where m and n are constants ,the quotient is x^2+2x+1 and the remainder is -8 .Find the value of m and n.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Perform the polynomial division! Using that and the given remainder, you can set up two equations.
.
.
system%28m=6%2Cn=-7%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


If you want to use up some spare time, do what the other tutor says: perform the long polynomial division to get two equations to solve for m and n.

There is a MUCH easier and more sensible way to find m and n.

The given polynomial is the divisor, multiplied by the quotient, plus the remainder.

%282x%2B1%29%28x%5E2%2B2x%2B1%29%2B%28-8%29
%282x%5E3%2Bx%5E2%2B4x%5E2%2B2x%2B2x%2B1%29-8
2x%5E3%2B5x%5E2%2B4x-7

ANSWERS: m = 4; n = -7