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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Solution

$p (x) = x^{4} - 3 x^{2} + 4 x + 5 = x^{4} + 0. x^{3} - 3 x^{2} + 4 x + 5$

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

$x^{2} + x - 3 x^{2} - x + 1 \sqrt{x^{4} + 0. x^{3} - 3 x^{2} + 4. x + 5} x^{4} - x^{3} + x^{2} - + - - --------- - x^{3} - 4 x^{2} + 4 x + 5 x^{3} - x^{2} + x - --------------- - - 3 x^{2} + 3 x + 5 - 3 x^{2} + 3 x - 3 + - + - --------------- - 8$

Quotient = $x^{2} + x - 3$ and 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 in each of the following:
(i)

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

(ii)

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

(iii)

p (x) = x^{4} - 5 x + 6, g (x) = 2 - x^{2}

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

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

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

$p (x) = x^{3} - 3 x^{2} + 5 x - 3$ and $g (x) = x^{2} - 2$ .

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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)=x4−3x2+4x+5,g(x)=x2+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: $p (x) = x^{4} - 3 x^{2} + 4 x + 5, g (x) = x^{2} + 1 - x$