Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

MEDIUM

Earn 100

Factorize: ${(a + b + c)}^{3} - a^{3} - b^{3} - c^{3}$ :

Important Questions on Factorisation and Identities

EASY

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Factorise

a^{3} - 7 a^{2} - 21 a + 27

by suitable arrangement.

MEDIUM

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Use trial and error method to factorise

5 a^{2} + 15 a + 3

MEDIUM

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Solve:

x^{3} - 5 x^{2} - 4 x + 20 = 0

.

MEDIUM

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Factorise

x^{4} + 3 x^{3} + 4 x^{2} + 3 x + 1

MEDIUM

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Use trial and error method to factorise

x^{3} - 7 x^{2} + 14 x - 8

EASY

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Factorise:

x^{4} + 3 x^{3} + 4 x^{2} + 3 x + 1

MEDIUM

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Factorise

4 x^{2} - 4 x y + y^{2} - 6 x + 3 y

HARD

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Factorise

a^{6} + 5 a^{3} + 8

.

MEDIUM

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Resolve into factors,

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

MEDIUM

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Show that the polynomial

5 x^{3} - 13 x^{2} + 17 x - 9

has exactly one real root.

MEDIUM

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Factorise

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

MEDIUM

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Factorise

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

EASY

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Factorise: $(p^{2} + q^{2}) x y + p q (x^{2} + y^{2})$

MEDIUM

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Factorise

(a + b + c) (b c + c a + a b) - a b c

by suitable arrangement.

HARD

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

The polynomial

x^{4} - 48 x^{2} - 21 x - 2

, is denoted by

p (x)

. Find the value of constant

k

for which

f (x) = (x^{2} + k x + 2) (x^{2} - k x - 1)

. Hence solve

f (x) = 0

. Give your answers in exact form.

EASY

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Factorise:

a^{2} + 2 b^{2} - 2 c^{2} + 3 a b + 3 b c + c a

EASY

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Cotyledons are also called-

HARD

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Factorise

x^{6} + 8 x^{3} + 27

.

EASY

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Factorise:

x^{2} + x y - 2 y^{2} + x + 5 y - 2

MEDIUM

Mathematics>Algebra>Factorisation and Identities>Factorisation of Algebraic Expression

Factorise

3 x^{3} + 2 x^{2} + 2 x + 3