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Standard X

Mathematics

Division Algorithm for a Polynomial

On dividing a...

Question

On dividing a polynomial p(x) by a nonzero polynomial q(x), let g(x) be the quotient and r(x) be the remainder then p(x) = q(x).g(x)+r(x), where

(a) r(x) = 0 always

(b) deg r(x) < deg g(x) always

(c) either r(x) = 0 or deg r(x) < deg g(x)

(d) r(x) = g(x)

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Solution

On dividing a polynomial p(x) by a nonzero polynomial q(x), let g(x) be the quotient and r(x) be the remainder then p(x) = q(x).g(x)+r(x), where either 0 or deg(r(x)) < deg(g(x)).

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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]

Say true or false:

For polynomials

p (x)

and any non-zero polynomial

g (x)

, there are polynomials

q (x)

and

r (x)

such that

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

, where

r (x) = 0

or degree

r (x) <

degree

g (x) .

This statement is correctly explains the remainder theorem.

Q. Who is correct?
Aakanksha:

q (x) = \frac{p (x) - r (x)}{g (x)}

Arjun:

q (x) = \frac{p (x)}{g (x)} - r (x)

Aman:

q (x) = p (x) - \frac{r (x)}{g (x)}

Anasuya:

q (x) = p (x) + \frac{r (x)}{g (x)}

Given,

p (x)

is the dividend,

g (x)

is the divisor,

q (x)

is the quotient, and

r (x)

is the remainder

Q. On dividing

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

by a polynomial

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

, the remainder

r (x) = 9 x + 10

. Find the quotient polynomial

q (x)

Q. If

p (x)

and

g (x)

are any two polynomials with

g (x) \neq 0

, then we can find polynomial

q (x)

and

r (x)

such that

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

where

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On dividing a polynomial p(x) by a nonzero polynomial q(x), let g(x) be the quotient and r(x) be the remainder then p(x) = q(x).g(x)+r(x), where (a) r(x) = 0 always (b) deg r(x) < deg g(x) always (c) either r(x) = 0 or deg r(x) < deg g(x) (d) r(x) = g(x)

On dividing a polynomial p(x) by a nonzero polynomial q(x), let g(x) be the quotient and r(x) be the remainder then p(x) = q(x).g(x)+r(x), where either 0 or deg(r(x)) < deg(g(x)).

On dividing a polynomial p(x) by a nonzero polynomial q(x), let g(x) be the quotient and r(x) be the remainder then p(x) = q(x).g(x)+r(x), where

(a) r(x) = 0 always

(b) deg r(x) < deg g(x) always

(c) either r(x) = 0 or deg r(x) < deg g(x)

(d) r(x) = g(x)