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Apply division algorithm to find the quotient $q(x)$ and remainder $r(x)$ on dividing $f(x)$ by $g(x)$ in the following:
$f(x)\ =\ 15x^3\ –\ 20x^2\ +\ 13x\ –\ 12,\ g(x)\ =\ x^2\ –\ 2x\ +\ 2$
Given: $f(x)\ =\ 15x^3\ –\ 20x^2\ +\ 13x\ –\ 12$ and $g(x)\ =\ x^2\ –\ 2x\ +\ 2$. To do: We have to find the quotient $q(x)$ and remainder $r(x)$ on dividing $f(x)$ by $g(x)$. Solution: Dividend$f(x)\ =\ 15x^3\ –\ 20x^2\ +\ 13x\ –\ 12$ Divisor$g(x)\ =\ x^2\ –\ 2x\ +\ 2$ $x^2 – 2x + 2$)$15x^3 – 20x^2 + 13x – 12$($15x+10$ $15x^3 - 30x^2 + 30x$ ------------------------------------ $10x^2 - 17x - 12$ $10x^2 - 20x + 20$ -------------------------- $3x - 32$ Therefore, $q(x)=15x+10$.
$r(x)=3x - 32$.
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