Mathematics: When 10x^3+mx^2- x+10 is divided by 5x-3, the quotient is 2x^2+no-2 and the remainder is 4. what is the value of m and n?

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When 10x^3+mx^2- x+10 is divided by 5x-3, the

jojo171717

15.01.2022

When 10x^3+mx^2- x+10 is divided by 5x-3 , the quotient is 2x^2+nx-2 and the remainder is 4.

The value of m=-21 and n=-3

Given :

When 10x^3+mx^2- x+10 is divided by 5x-3 , the quotient is 2x^2+nx-2 and the remainder is 4.

We frame equation using quotient and remainder

Dividend = quotient (divisor)+ remainder

$10x^3+mx^2- x+10=(2x^2+nx-2)(5x-3)+4\\10x^3+mx^2- x+10=10x^3-6x^2+5nx^2-3nx-10x+6+4\\\\10x^3+mx^2- x+10=10x^3+x^2(5n-6)+x(-3n-10)+10\\\\$

Now we make x^2 parts are equal and solve for m and n

Also we make x parts are equal

$-3n-10=-1\\-3n=-1+10\\-3n=9\\n=-3$

Now make x^2 terms equal

$5n-6=m\\5(-3)-6=m\\m=-21$

The value of m and n are

m=-21 and n=-3

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