All In One ICSE Mathematics Class 10>Chapter 7 - Factorisation of Polynomials>Topic Exercise>Q 1

EASY

10th ICSE

IMPORTANT

Earn 100

Using factor theorem, check whether the polynomial $g (x) = x - 2$ is a factor of $f (x) = x^{3} - 4 x^{2} + x + 6$ or not.

Important Questions on Factorisation of Polynomials

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 7 - Factorisation of Polynomials>Topic Exercise>Q 2

If

(x + 2)

and

(x + 3)

are the factors

x^{3} + a x + b

, find the value of

a + b

.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 7 - Factorisation of Polynomials>Topic Exercise>Q 3

Find the value of

' k'

if

(x - 2)

is a factor of

x^{3} + 2 x^{2} - k x + 10

. Hence, determine whether

(x + 5)

is also a factor.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 7 - Factorisation of Polynomials>Topic Exercise>Q 4

For

a = \frac{k}{3}

, the polynomial

g (x)

is a factor of

f (x)

, where

f (x) = x^{3} + a (x^{2} + 1) - 2 x + 4, g (x) = x + a

. Find

k

.

EASY

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 7 - Factorisation of Polynomials>Topic Exercise>Q 5

What must be subtracted from

16 x^{3} - 8 x^{2} + 4 x + 7

, so that the resulting expression has

(2 x + 1)

as a factor?

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 7 - Factorisation of Polynomials>Topic Exercise>Q 6

Show that

(x - 2)

is a factor of

7 x^{2} - 10 x - 8

. Hence, factorize

7 x^{2} - 10 x - 8

.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 7 - Factorisation of Polynomials>Topic Exercise>Q 7

Show that

(2 x + 7)

is a factor of

2 x^{3} + 7 x^{2} - 4 x - 14

. Hence, factorise

2 x^{3} + 7 x^{2} - 4 x - 14

.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 7 - Factorisation of Polynomials>Topic Exercise>Q 8

Use factor theorem to factorise completely

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

.

EASY

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 7 - Factorisation of Polynomials>Topic Exercise>Q 9

Use factor theorem to factorise the polynomial

x^{3} - 13 x - 12

completely. Hence, solve the corresponding polynomial equation.