MATHEMATICS>Chapter 2 - Polynomials>EXERCISE 2.3>Q 7

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9th CBSE

IMPORTANT

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Using remainder theorem, find the remainder when $x^{3} + 3 x^{2} + 3 x + 1$ is divided by $(x - \frac{1}{2})$ .

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Important Questions on Polynomials

MEDIUM

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 2 - Polynomials>EXERCISE 2.3>Q 8

Divide

x^{3} + 1

by

x + 1

using long division method and verify it by remainder theorem.

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9th CBSE

IMPORTANT

MATHEMATICS>Chapter 2 - Polynomials>EXERCISE 2.3>Q 9

Without actual division, find the remainder when

5 x^{3} - x^{2} + 6 x - 2

is divided by

1 - 5 x

.

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9th CBSE

IMPORTANT

MATHEMATICS>Chapter 2 - Polynomials>EXERCISE 2.3>Q 10

Find the value of

k

if the polynomial

P (x) = 3 x^{3} + k x^{2} + 5 x - 16

is divided by

(x - 2)

leaves a remainder

- 8

.

HARD

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 2 - Polynomials>EXERCISE 2.3>Q 11

The polynomial

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

when divided by

x + 1

leaves the remainder

19

. Find the value of

a

. Also find the remainder when

p (x)

is divided by

x + 2

.

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9th CBSE

IMPORTANT

MATHEMATICS>Chapter 2 - Polynomials>EXERCISE 2.3>Q 12

If the polynomial

P (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + 8

is divided by

(x - 2)

, it leaves a remainder

10 .

Find the value of

‘ a ’

.

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9th CBSE

IMPORTANT

MATHEMATICS>Chapter 2 - Polynomials>EXERCISE 2.3>Q 13

If the polynomial

a x^{3} + 4 x^{2} + 3 x - 4

and

x^{3} - 4 x + a

are divided by

(x - 3)

then the remainder in each case is same. Find the value of

a

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9th CBSE

IMPORTANT

MATHEMATICS>Chapter 2 - Polynomials>EXERCISE 2.3>Q 14

Check whether the polynomial

P (x) = 4 x^{3} + 4 x^{2} - x - 1

is a multiple of

(2 x + 1) .

HARD

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 2 - Polynomials>EXERCISE 2.3>Q 15

If

f (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + 8

is a polynomial such that when it is divided by

(x - 1),

the remainder is

5

. Determine the remainder when

f (x)

is divided by

(x - 2)

and

(x - 1) .