document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #834553 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "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.

\n" ); document.write( "There is a MUCH easier and more sensible way to find m and n.

\n" ); document.write( "The given polynomial is the divisor, multiplied by the quotient, plus the remainder.

\n" ); document.write( " $\"%282x%2B1%29%28x%5E2%2B2x%2B1%29%2B%28-8%29\"$
\n" ); document.write( " $\"%282x%5E3%2Bx%5E2%2B4x%5E2%2B2x%2B2x%2B1%29-8\"$
\n" ); document.write( " $\"2x%5E3%2B5x%5E2%2B4x-7\"$

\n" ); document.write( "ANSWERS: m = 4; n = -7

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