All In One ICSE Mathematics Class 10>Chapter 7 - Factorisation of Polynomials>CHAPTER EXERCISE>Q 15

MEDIUM

10th ICSE

IMPORTANT

Earn 100

If $(y - p)$ is a common factor of the polynomials $f (y) = y^{2} + a y + b$ and $g (y) = y^{2} + m y + n$ , then show that $p = \frac{n - b}{a - m}$ .

Important Questions on Factorisation of Polynomials

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 7 - Factorisation of Polynomials>CHAPTER EXERCISE>Q 16

Find the value of constants

a a n d b

,

(x - 2) a n d (x + 3)

are both factors of the expression

x^{3} + a x^{2} + b x - 12

.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 7 - Factorisation of Polynomials>CHAPTER EXERCISE>Q 17

Find

b a n d c

such that,

(y + 1) a n d (y + 2)

are the factors of the polynomial

y^{3} + b y^{2} - c y + 10

.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 7 - Factorisation of Polynomials>CHAPTER EXERCISE>Q 18

(x - 2)

is a factor of expression

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

. When this expression is divided by

(x - 3)

, it leaves the remainder

3

. Find the values of

a a n d b

.

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 7 - Factorisation of Polynomials>CHAPTER EXERCISE>Q 19

Show that

(2 x + 3)

is a factor of

4 x^{3} + 20 x^{2} + 33 x + 18

. Hence, factorise the given polynomial completely by using factor theorem.

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 7 - Factorisation of Polynomials>CHAPTER EXERCISE>Q 20

Show that

(2 x + 7)

is a factor of

2 x^{3} + 5 x^{2} - 11 x - 14

. Hence, factorise the given polynomial completely by using factor theorem.

EASY

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 7 - Factorisation of Polynomials>CHAPTER EXERCISE>Q 21

Show that

(3 z + 10)

is a factor of

9 z^{3} - 27 z^{2} - 100 z + 300

. Factorize the given polynomial completely by using factor theorem.

(3 z + 10)

is a factor of it.

EASY

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 7 - Factorisation of Polynomials>CHAPTER EXERCISE>Q 22

Factories

x^{3} - 23 x^{2} + 142 x - 120

, using factor theorem.

EASY

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 7 - Factorisation of Polynomials>CHAPTER EXERCISE>Q 23

Using factor theorem, factorize the polynomial

x^{3} + 6 x^{2} + 11 x + 6

. Hence, solve the given polynomial equation