Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder of the following.
$p (x) = x^{4} - 3 x^{2} + 4 x + 5$ , $g (x) = x^{2} + 1 - x$ .

x^{2} + x + 3, 8

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x^{2} - x - 3, 8

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x^{2} - 3, 8

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x^{2} + x - 3, 8

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Solution

The correct option is D $x^{2} + x - 3, 8$
$P (x) = x^{4} - 3 x^{2} + 4 x + 5$
$g (x) = x^{2} + 1 - x$

$\frac{P (x)}{g (x)} = \frac{x^{4} - 3 x^{2} + 4 x + 5}{x^{2} + 1 - x}$

$x^{2} + x - 3 x^{2} - x + 1) ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ x^{4} - 3 x^{2} + 4 x + 5 x^{4} - x^{3} + x^{2}_____________x^{3} - 4 x^{2} + 4 x x^{3} - x^{2} + x_- 3 x^{2} + 3 x + 5 - 3 x^{2} + 3 x - 3______________8$

Quotient $= x^{2} + x - 3$
Remainder $= 8$

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Similar questions

Q. Divide the polynomial

p (x)

by the polynomial

g (x)

and find the quotient and remainder.

p (x) = x^{4} - 3 x^{2} + 4 x + 5

g (x) = x^{2} + 1 - x

Question 1 (ii)
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: $p (x) = x^{4} - 3 x^{2} + 4 x + 5, g (x) = x^{2} + 1 - x$

Question 1 (ii)
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
$p (x) = x^{4} - 3 x^{2} + 4 x + 5, g (x) = x^{2} + 1 - x$

Q. Find the remainder when

p (x) = x^{4} - 3 x^{2} + 4 x + 5

, is divided by

g (x) = x^{2} + 1 - x

Q. A polynomial

p (x)

is divided by

g (x)

, the obtained quotient

q (x)

and the remainder

r (x)

are given in the table. Find

p (x)

in each case.

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	?	$x^{2} + 2 x + 1$	$x^{4} - 2 x^{2} + 5 x - 7$	$4 x + 12$

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Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder of the following.p(x)=x4−3x2+4x+5, g(x)=x2+1−x.

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder of the following.
$p (x) = x^{4} - 3 x^{2} + 4 x + 5$ , $g (x) = x^{2} + 1 - x$ .