Divide the polynomial $p\left(x\right)$ by the polynomial $g\left(x\right)$ and find the quotient and remainder of the following.

$p\left(x\right)=x^3-3x^2+5x-3$ and $g\left(x\right)=x^2-2$.

Q. Divide the polynomial $p\left(x\right)$ by the polynomial $g\left(x\right)$ and find the quotient and remainder in each of the following:
(i) $p\left(x\right)=x^3-3x^2+5x-3,g\left(x\right)=x^2-2$
(ii) $p\left(x\right)=x^4-3x^2+4x+5,g\left(x\right)=x^2+1-x$
(iii) $p\left(x\right)=x^4-5x+6,g\left(x\right)=2-x^2$

Q.

Question 1 (i)
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

$p\left(x\right)=x^3-3x^2+5x-3,g\left(x\right)=x^2-2$

Q. On dividing the polynomial $p\left(x\right)=x^3-3x^2+x+2$ by a polynomial $g\left(x\right)$, the quotient and remainder were $(x-2)$ and $(-2x+4)$ respectively. Find $g\left(x\right)$

Q.

Question 1 (i)
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

$p\left(x\right)=x^3-3x^2+5x-3,g\left(x\right)=x^2-2$

Q. A polynomial $p\left(x\right)$ is divided by $g\left(x\right)$, the obtained quotient $q\left(x\right)$ and the remainder $r\left(x\right)$ are given in the table. Find $p\left(x\right)$ in each case.

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