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Standard X

Mathematics

Division Algorithm for a Polynomial

On dividing f...

Question

On dividing f(x) = x³ - 3x² + x + 2 by a polynomial g(x) the quotient and remainder q(x) and r(x) are (x – 2) and (-2x + 4) respectively, then g(x) is

x² - x + 1

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x² + x - 1

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2x² - 1 + x

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x² + x - 3

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Solution

The correct option is A
x² - x + 1

f(x) = g(x) q(x) + r(x)

To get g(x), divide f(x) – r(x) by q(x).

Hence, g(x) = x² - x + 1

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Similar questions

Q. On dividing the polynomial

f (x) = x^{3} - 3 x^{2} + x + 2

by a polynomial

g (x)

, the quotient

q (x)

and remainder

r (x)

are x-2 and -2x+4 respectively. Find the polynomial

g (x)

. [4 MARKS]

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

Q. On dividing

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

by a polynomial

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, where

g (x) = x^{3} + x^{2} + x + 1

, the quotient obtained as

2 x^{2} + x + 1

. Find the remainder

r (x)

Q. On dividing

f (x)

by a polynomial

x - 1 - x^{2}

, the quotient

q (x)

and remainder

r (x)

are

(x - 2)

and

3

respectively. Then

f (x)

Q. Find the quotient

q (x)

and remainder

r (x)

of the following when

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f (x) = x^{3} - 3 x^{2} - x + 3

;

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

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On dividing f(x) = x³ - 3x² + x + 2 by a polynomial g(x) the quotient and remainder q(x) and r(x) are (x – 2) and (-2x + 4) respectively, then g(x) is

The correct option is A x² - x + 1f(x) = g(x) q(x) + r(x) To get g(x), divide f(x) – r(x) by q(x). Hence, g(x) = x² - x + 1

The correct option is A
x² - x + 1

f(x) = g(x) q(x) + r(x)

To get g(x), divide f(x) – r(x) by q(x).

Hence, g(x) = x² - x + 1