## Polynomial division and unknowns

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
mrwisdom
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### Polynomial division and unknowns

when 10x^3 +mx^2 -x +10 is divided by 5x-3, the quotient is 2x^2 +nx - 2 and the remainder is 4. find the values of m and n

nona.m.nona
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### Re: Polynomial division and unknowns

when 10x^3 +mx^2 -x +10 is divided by 5x-3, the quotient is 2x^2 +nx - 2 and the remainder is 4. find the values of m and n
What expressions did you get for the quotient and the remainder when you did the long division? When you set your expressions equal to the given expression and value, where did this lead?

Thank you.

mrwisdom
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### Re: Polynomial division and unknowns

im not sure i understand what you mean.

Martingale
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### Re: Polynomial division and unknowns

when 10x^3 +mx^2 -x +10 is divided by 5x-3, the quotient is 2x^2 +nx - 2 and the remainder is 4. find the values of m and n
$\frac{10x^3+mx^2-x+10}{5x-3}=2x^2+nx-2+\frac{4}{5x-3}$

$2x^2+nx-2+\frac{4}{5x-3}=\frac{(2x^2+nx-2)(5x-3)}{5x-3}+\frac{4}{5x-3}=\frac{(2x^2+nx-2)(5x-3)+4}{5x-3}$

thus

$10x^3+mx^2-x+10=(2x^2+nx-2)(5x-3)+4$

expand and solve for $n$. Then you will be able to get $m$