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Zeroes of a Polynomial

If the polyno...

Question

If the polynomial $p (x) = x^{4} - 3 x^{2} + 5 x + 3$ is divided by $x^{2} - 2$ the remainder is $a x + b$ what will be the quotient? Find also the value of $a$ and $b$ .

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Solution

When we divide
$x^{4} - 3 x^{2} + 5 x + 3$ by $x^{2} - 2$
Quotient is $x^{2} - 1$
and the remainder is $5 x + 1$
ATQ :-
Remainder is $a x + b$
implies that
$a = 5, b = 1$

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Similar questions

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

(i)

(ii)

(iii)

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

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

p (x)

q (x)

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

p (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + 3 a - 7

x + 1

19

a

p (x)

x + 2

p (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + 3 a - 7

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