Divided the polynomial p (x) by the polynomial g (x) and find the quotient and remainder in each of the following
$p (x) = x^{4} - 3 x^{3} + 4 x + 5 g (x) = x^{3} + 1 - x$

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Solution

$p (x) = x^{4} - 3 x^{3} + 4 x + 5 g (x) = x^{3} + 1 - x \Rightarrow x^{2} - x + 1$
let us divided $x^{4} - 3 x^{2} + 4 x + 5 b y x^{2} - x + 1 x^{2} - x + 1) x^{4} + 0 - 3 x^{2} + 4 x (x^{2} - x + 1 x^{4} - x^{3} + x^{2}$
- + -..........................
$x^{3} - 4 x^{2} + 4 x + 5 x^{3} - x^{2} + x$ - + - ........................
$3 x^{2} + 3 x + 5 - 3 x^{2} + 3 x - 3$ - + -...........................................
8 $x^{4} - 3 x^{2} + 4 x + 5 = (x^{2} - x + 1) (x^{2} + x - 3) + 8$ $∴$ The quotient = $x^{2} + x - 3$
The remainder = 8

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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. 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

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:
$p (x) = x^{4} - 3 x^{2} + 4 x + 5, g (x) = x^{2} + 1 - x$

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Divided the polynomial p (x) by the polynomial g (x) and find the quotient and remainder in each of the followingp(x)=x4−3x3+4x+5g(x)=x3+1−x

Divided the polynomial p (x) by the polynomial g (x) and find the quotient and remainder in each of the following
$p (x) = x^{4} - 3 x^{3} + 4 x + 5 g (x) = x^{3} + 1 - x$