Apply division algorithm to find the quotient $q(x)$ and remainder $r(x)$ on dividing $f(x)$ by $g(x)$ in the following:
$f(x)\ =\ x^3\ –\ 6x^2\ +\ 11x\ –\ 6,\ g(x)\ =\ x^2\ +\ x\ +\ 1$
Given:
$f(x)\ =\ x^3\ –\ 6x^2\ +\ 11x\ –\ 6$ and $g(x)\ =\ x^2\ +\ x\ +\ 1$.
To do:
We have to find the quotient $q(x)$ and remainder $r(x)$ on dividing $f(x)$ by $g(x)$.
Solution:
Dividend$f(x)\ =\ x^3\ –\ 6x^2\ +\ 11x\ –\ 6$
Divisor$g(x)\ =\ x^2\ +\ x\ +\ 1$
$x^2+x+1$)$x^3-6x^2+11x-6$($x-7$
$x^3+ x^2 + x$
--------------------------
$-7x^2+10x-6$
$-7x^2 - 7x -7$
-------------------------
$17x+1$
Therefore,
$q(x)=x-7$.
$r(x)=17x+1$.
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