Sl.	$p (x)$	$g (x)$	$q (x)$	$r (x)$
i	?	$x - 2$	$x^{2} - x + 1$	$4$
ii	?	$x + 3$	$2 x^{2} + x + 5$	$3 x + 1$
iii	?	$2 x + 1$	$x^{3} + 3 x^{2} - x + 1$	$0$
iv	?	$x - 1$	$x^{3} - x^{2} - x - 1$	$2 x - 4$
v	?	$x^{2} + 2 x + 1$	$x^{4} - 2 x^{2} + 5 x - 7$	$4 x + 12$

On dividing a polynomial p(x) by a nonzero polynomial q(x), let g(x) be the quotient and r(x) be the remainder then p(x) = q(x).g(x)+r(x), where

(a) r(x) = 0 always

(b) deg r(x) < deg g(x) always

(d) r(x) = g(x)

$p (x) = x^{3} + 8 x^{2} - 7 x + 12$ and $g (x) = x - 1$ . If $p (x)$ is divided by $g (x)$ , it gives $q (x)$ and $r (x)$ as quotient and remainder respectively. If $a$ is the degree of $q (x)$ and $b$ is the degree of $r (x)$ , then, $(a - b) = ?$ .

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Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder. p(x)=x3−3x2+5x−3g(x)=x2−2

The correct option is C q(x)=x−3,r(x)=7x−9p(x)=x3−3x2+5x−3=x3−3x2−2x+6+7x−9⇒p(x)=(x−3)(x2−2)+(7x−9)g(x)=x2−2Dividing p(x) by g(x), we getQuotient q(x)=(x−3) and Remainder, R(x)=(7x−9)Hence, option D.

Divide the polynomial $p (x)$ by the polynomial $g (x)$ and find the quotient and remainder.
$p (x) = x^{3} - 3 x^{2} + 5 x - 3$
$g (x) = x^{2} - 2$