Apply division algorithm to find the quotient $q(x)$ and remainder $r(x)$ on dividing $f(x)$ by $g(x)$ in the following:
$f(x)\ =\ 4x^3\ +\ 8x^2\ +\ 8x\ +\ 7,\ g(x)\ =\ 2x^2\ –\ x\ +\ 1$
Given:
$f(x)\ =\ 4x^3\ +\ 8x^2\ +\ 8x\ +\ 7$ and $g(x)\ =\ 2x^2\ –\ x\ +\ 1$.
To do:
We have to find the quotient $q(x)$ and remainder $r(x)$ on dividing $f(x)$ by $g(x)$.
Solution:
Dividend$f(x)\ =\ 4x^3\ +\ 8x^2\ +\ 8x\ +\ 7$
Divisor$g(x)\ =\ 2x^2\ –\ x\ +\ 1$
$x^2 – x + 1$)$4x^3 + 8x^2 + 8x + 7$($2x+5$
$4x^3 - 2x^2 +2x$
-----------------------------
$10x^2+6x+7$
$10x^2-5x+5$
-------------------
$11x+2$
Therefore,
$q(x)=2x+5$.
$r(x)=11x+2$.
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