# 8th Class Mathematics Factorisation Question Bank

### done Factorisation

• A) $(y-p)(x+q)$

B) $(y-p)(x-q)$

C) $(y+p)(x+q)$

D) $(y+p)(x-q)$

• A) ${{x}^{2}}-3x$

B) $3x$

C) ${{x}^{2}}+5$

D) Both (a) and (b)

• A) $\left( \frac{x}{4}+\frac{y}{9} \right)\left( \frac{x}{4}-\frac{y}{9} \right)$

B) $\left( \frac{x}{2}+\frac{y}{9} \right)\left( \frac{x}{2}-\frac{y}{9} \right)$

C) $\left( \frac{x}{2}+\frac{y}{3} \right)\left( \frac{x}{2}-\frac{y}{3} \right)$

D) Both (a) and (b)

• A) $(3x-4)(5x+2)$

B) $(3x-4)(5x-2)$

C) $(3x+4)(5x-2)$

D) $(3x+4)(5x+2)$

• A) $({{x}^{2}}+2)({{x}^{2}}-2)$

B) $(x+4)(x-4)$

C) $(x+2)(x-2)$

D) Does not exist

• A) $\left( x-3\sqrt{3} \right)\left( \sqrt{3}x+2 \right)$

B) $\left( x-3\sqrt{3} \right)\left( \sqrt{3}x-2 \right)$

C) $\left( x+3\sqrt{3} \right)\left( \sqrt{3}x-2 \right)$

D) $\left( x+3\sqrt{3} \right)\left( \sqrt{3}x+2 \right)$

• A) $(2x+z)(2{{x}^{3}}+{{z}^{3}}-2{{x}^{2}})$

B) $z(x+2z)({{x}^{2}}+{{z}^{2}}-{{x}^{2}})$

C) $z(2x-z)(2{{x}^{2}}-2xz+{{z}^{2}})$

D) $z(x-2z)(2{{z}^{2}}-2xz+{{x}^{2}})$

• A) $(x+y+z)(x+y-z)$

B) $(y-y-z)(x+y-z)$

C) $(x-y+z)(x+y-z)$

D) None of these

• A) $({{x}^{2}}+{{y}^{2}})({{x}^{2}}+{{y}^{2}}-xy)$

B) $({{x}^{2}}+{{y}^{2}})({{x}^{2}}-{{y}^{2}})$

C) $({{x}^{2}}+{{y}^{2}}+xy)({{x}^{2}}+{{y}^{2}}-xy)$

D) Factorisation is not possible

• A) -2, 5

B) 5, 25

C) 10, 20

D) 6, 25

• A) $(2b-3a)$

B) $(3a-b)$

C) $(4a-3b)$

D) $(-3a+4b)$

• A) $4{{x}^{3}}{{y}^{2}}+2x{{y}^{3}}$

B) $4{{x}^{3}}y-2x{{y}^{3}}$

C) $-4{{x}^{2}}{{y}^{2}}+2x{{y}^{3}}$

D) $-4x{{y}^{2}}+2x{{y}^{3}}$

• A) $(p+q+a+b)$

B) $(p+q-a+b)$

C) $(p-q+a-b)$

D) $(p-q+a+b)$

• A) $4(2x+3y)(x+y-2)$

B) $4(2x+3y)(x+y+2)$

C) $(2x-3y+7)(2x-3y+2)$

D) $(2x+3y-7)(2x+3y+2)$

• A) ${{x}^{3}}(-7{{x}^{7}}y+4z)$

B) ${{x}^{2}}(7{{x}^{7}}y-4z)$

C) ${{x}^{2}}(-7{{x}^{6}}y+2z)$

D) ${{x}^{3}}(-7{{x}^{7}}y+4z)$

•  (i) $(2{{a}^{2}}+8a+3)$ (ii) $(6{{a}^{2}}+52a-5)$ (iii) $\text{(3a+5)}$

A) Only (i)

B) Both (i) and (ii)

C) Only (ii)

D) All (i), (ii) and (iii)

•  (i) $\frac{{{a}^{2}}-{{b}^{2}}}{a(a-b)}-\frac{a{{b}^{2}}+{{a}^{2}}b}{a{{b}^{2}}}$ is equal to P . (ii) $\frac{64{{y}^{4}}+8{{y}^{3}}}{4{{y}^{3}}}$ is equal to Q . (iii) When we divide $(38{{a}^{3}}{{b}^{3}}{{c}^{2}}-19{{a}^{4}}{{b}^{2}}c)$ by $19{{a}^{2}}bc$, the result is $ka{{b}^{2}}c-{{a}^{2}}b$. Then $k=\underline{\,\,\,R\,\,\,}$.

A)

 P Q R $\frac{(a+b)(b-a)}{ab}$ $3(8y+1)$ 1

B)

 P Q R $\frac{(a+b\,)(b-a)}{ab}$ $3(8y+1)$ 1

C)

 P Q R $\frac{(a+b)(a-b)}{ab}$ $2(8y+1)$ 1

D)

 P Q R $\frac{(a+b)(b-a)}{ab}$ $2(8y+1)$ 2

• A) The factors of an expression are always either algebraic variable or algebraic expression.

B) An irreducible factor is a factor that cannot be expressed further as a product of factors.

C) Every binomial expression can be factorised into two monomial expression.

D) The process of writing a given expression as the product of two or more factors is called multiplication of factors.

•  Column - I Column - II P. $9{{x}^{2}}+24x+16$ (i) $(2x-4)$ Q. $25{{x}^{2}}+30x+9$ (ii) $(4x+1)$ R. $40{{x}^{2}}+14x+1$ (iii) $(5x+3)$ S. $4{{x}^{2}}-16x+16$ (iv) $(3x+4)$

A) P$\to$(iv); Q$\to$(iii); R$\to$(ii); S$\to$(i)

B) P$\to$(iii): Q$\to$(i); R$\to$(iv); S$\to$(ii)

C) P$\to$(ii); Q$\to$(i); R$\to$(iv): S$\to$(iii)

D) P$\to$(iv); Q$\to$(iii); R$\to$(i); S$\to$(ii)

•  (i) Factorise: ${{x}^{2}}+\frac{1}{{{x}^{2}}}-3$ (ii) Find the greatest common factors of $14{{x}^{2}}{{y}^{3}},21{{x}^{3}}{{y}^{2}}$ and $35{{x}^{4}}{{y}^{5}}z$. (iii) Divide $z(5{{z}^{2}}-80)$by $5z(z+4)$.

A)

 (i) (ii) (iii) $\left( x-\frac{1}{x} \right)\left( x-\frac{1}{x}-2 \right)$ $7x{{y}^{2}}$ $z-4$

B)

 (i) (ii) (iii) $\left( x+\frac{1}{x} \right)\left( x+\frac{1}{x}+2 \right)$ $7{{x}^{2}}y$ $z-4$

C)

 (i) (ii) (iii) $\left( x-\frac{1}{x}+1 \right)\left( x-\frac{1}{x}-1 \right)$ $7{{x}^{2}}{{y}^{2}}$ $z-4$

D)

 (i) (ii) (iii) $\left( x-\frac{1}{x}-1 \right)\left( x+\frac{1}{x}+1 \right)$ $7{{x}^{2}}{{y}^{2}}$ $z-2$