## Polynomial division and unknowns

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.

### 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
mrwisdom

Posts: 8
Joined: Thu Oct 08, 2009 2:39 am

### Re: Polynomial division and unknowns

mrwisdom wrote: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.
nona.m.nona

Posts: 249
Joined: Sun Dec 14, 2008 11:07 pm

### Re: Polynomial division and unknowns

im not sure i understand what you mean.
mrwisdom

Posts: 8
Joined: Thu Oct 08, 2009 2:39 am

### Re: Polynomial division and unknowns

mrwisdom wrote: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 $m$

Martingale

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Location: USA