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Standard VIII

Mathematics

Division of a Polynomial by a Polynomial

On dividing t...

Question

On dividing the polynomial $9 x^{4} - 4 x^{2} + 5$ by another polynomial $3 x^{2} + x - 1$ , the remainder comes out to be $a x - b$ ,. Find $^{'} a^{'}$ and $^{'} b^{'}$ .

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Solution

By the help of long division method
$3 x^{2} + x - 1) 9 x^{4} - 4 x^{2} + 5 (3 x^{2} - x$

$- 9 x^{4} + 3 x^{2} - 3 x^{3}$
$- - - - - - - - - -$
$- 3 x^{3} - x^{2} + 4$
$+ 3 x^{2} + x^{2} - 4$
$- - - - - - - - - -$
$- x + 4$
Now,
$a x - b = - x + 4$
So, $A = - 1$ and $b = - 4$
which is the required answer.

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On dividing the polynomial 9x4−4x2+5 by another polynomial 3x2+x−1, the remainder comes out to be ax−b,. Find ′a′ and ′b′.

By the help of long division method 3x2+x−1)9x4−4x2+5(3x2−x −9x4+3x2−3x3 −−−−−−−−−− −3x3−x2+4 +3x2+x2−4 −−−−−−−−−− −x+4Now,ax−b=−x+4So, A=−1 and b=−4which is the required answer.

On dividing the polynomial $9 x^{4} - 4 x^{2} + 5$ by another polynomial $3 x^{2} + x - 1$ , the remainder comes out to be $a x - b$ ,. Find $^{'} a^{'}$ and $^{'} b^{'}$ .