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

MEDIUM

9th CBSE

IMPORTANT

Earn 100

Check whether the polynomial $P (x) = 4 x^{3} + 4 x^{2} - x - 1$ is a multiple of $(2 x + 1) .$

Important Questions on Polynomials

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) .

HARD

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 2 - Polynomials>EXERCISE 2.3>Q 16

The polynomial

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

when divided by

(x - 2)

and

(x + 2)

leaves the remainder

20

and

8

respectively. Find the value of

a

and

b .

Hence, find the remainder when

p (x)

is divided by

(x - 1) .

HARD

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 2 - Polynomials>EXERCISE 2.3>Q 17

Let

R_{1}

and

R_{2}

are the remainder when the polynomial

4 x^{3} + 3 x^{2} - 12 a x - 5

and

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

are divided by

(x - 1)

and

(x + 2)

respectively. if

3 R_{1} + R_{2} = - 28

, find the value of

' a'

HARD

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 2 - Polynomials>EXERCISE 2.3>Q 18

The polynomial

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

and

2 x^{3} - 5 x + a

when divided by

(x - 2)

leaves the remainder

p

and

q

respectively. If

p - 2 q = 4 .

Find the value of

a .

MEDIUM

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 2 - Polynomials>EXERCISE 2.3>Q 19

The polynomial

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

and

2 x^{3} - 5 x + a

when divided by

(x - 4)

leave the same remainder in each case. Find the value of

a .

EASY

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 2 - Polynomials>EXERCISE 2.4>Q 1

Show that

(x - 3)

is the factor of the polynomial

x^{3} - 3 x^{2} + 4 x - 12

.

EASY

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 2 - Polynomials>EXERCISE 2.4>Q 2

Show that

(x + 3)

is the factor of the polynomial

69 + 11 x - x^{2} + x^{3}

.

EASY

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 2 - Polynomials>EXERCISE 2.4>Q 2

Show that

(2 x - 3)

is the factor of the polynomial

x + 2 x^{3} - 9 x^{2} + 12

.