Apply division algorithm to find the quotient $q(x)$ and remainder $r(x)$ on dividing $f(x)$ by $g(x)$ in the following:
$f(x)\ =\ 10x^4\ +\ 17x^3\ –\ 62x^2\ +\ 30x\ –\ 3,\ g(x)\ =\ 2x^2\ +\ 7x\ +\ 1$
Given:
$f(x)\ =\ 10x^4\ +\ 17x^3\ –\ 62x^2\ +\ 30x\ –\ 3$ and $g(x)\ =\ 2x^2\ +\ 7x\ +\ 1$.
To do:
We have to find the quotient $q(x)$ and remainder $r(x)$ on dividing $f(x)$ by $g(x)$.
Solution:
Dividend$f(x)\ =\ 10x^4\ +\ 17x^3\ –\ 62x^2\ +\ 30x\ –\ 3$
Divisor$g(x)\ =\ 2x^2\ +\ 7x\ +\ 1$
$2x^2+7x+1$)$10x^4+17x^3-62x^2+30x-3$($5x^2-9x-2$
$10x^4+35x^3+5x^2$
---------------------------------------
$-18x^3-67x^2+30x-3$
$-18x^3-63x^2-9x$
-------------------------------
$-4x^2+39x-3$
$-4x^2-14x-2$
------------------------
$53x-1$
Therefore,
$q(x)=5x^2-9x-2$.
$r(x)=53x-1$.
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