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Standard IX

Mathematics

What will be ...

Question

What will be the remainder when a polynomial $q (x)$ of degree n (n>1) is divided by a polynomial $p (x) = x - a$ which is a factor of $q (x)$ ?

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x + a

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0.0

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Solution

The correct option is C 0.0
When a polynomial is divided by one its factors, the remainder is Zero because the polynomial is perfectly divisible by the factor.

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Similar questions

Q. The remainder on dividing the polynomial

q (x)

(x - a)

k

and the remainder on dividing the polynomial

r (x)

(x - a)

- k

.
(a) Find

q (a)

.
(b) Prove that

(x - a)

is a factor of the polynomial

q (x) + r (x)

Q. If the remainder when

p (x)

is divided by

x - 2

is a zero of the polynomial

q (x) = 2 x^{2} - 1

, what is the value of

p (2)

, if p(2) > 0 ?

Q. The remainder when

p (x) = 4 x - 5

is divided by

x - 3

is a zero of the polynomial

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

. What is the value of

a

Q. The polynomial

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

and

q (x) = x^{3} - 4 x + a

leave same remainder when divided by

(x - 3)

. Find

a

and hence find the remainder when

p (x)

is divided by

(x - 2) .

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

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

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Standard IX Mathematics

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What will be the remainder when a polynomial q(x) of degree n (n>1) is divided by a polynomial p(x)=x−a which is a factor of q(x) ?

The correct option is C 0.0When a polynomial is divided by one its factors, the remainder is Zero because the polynomial is perfectly divisible by the factor.

What will be the remainder when a polynomial $q (x)$ of degree n (n>1) is divided by a polynomial $p (x) = x - a$ which is a factor of $q (x)$ ?

The correct option is C 0.0
When a polynomial is divided by one its factors, the remainder is Zero because the polynomial is perfectly divisible by the factor.