Taking Out Common Factors

Q.

Factorize the given equation $2y^3+y^2-2y-1$.

Q. Sum of two numbers is 35 and their difference is 13. Find the smaller number.

1. 11

Q.

Factorise:

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

Q.

Factorise:

$a(a+b{)}^3-3a^{2}b(a+b)$

Q.

What is the factored form of $3x+24y$?

1. $3(x+8y)$

2. $3xy(x+8y)$

3. $3(3x+24y)$

4. $3xy(3x+24y)$

Q. Factorize: $x^3(2x-3y)-x^2(2x-3y{)}^2$

1. $x^2(2x-3y)(3y-x)$
2. $x^3(2x-3y)(3y-x)$
3. $x^2(2x-3y)(x-3y)$
4. $x(2x-3y)(3y-x)$

Q. Factorize: $2(2x-5y)(3x+4y)-6(2x-5y)(x-y)$

1. $2(2x-5y)\left(7y\right)$
2. $2(2x-5y)(4y+3x)$
3. $(2x-5y)\left(7y\right)$
4. $2(2x+5y)\left(7y\right)$

Q. The degree of the quotient when $6x^3+3x$ is divided by $3x$ is

1. 1
2. 2
3. 3
4. 4

Q. Factorize: $a^3+a-3a^2-3$

1. $(a^2+1)(a-3)$
2. $(a+1)(a-3)$
3. $(a^2+1)(a^2+3)$
4. $(a+1)(a-3{)}^2$

Q. Factorize: $16(a+b{)}^2-4a-4b$

1. $4(a+b)(4a+4b+1)$
2. $4(a+b)(4a-4b-1)$
3. $16(a+b)(a+b-1)$
4. $4(a+b)(4a+4b-1)$

Q. Match the following with their answers.

1. $1+x^2$
2. $x^2$
3. $x^4$
4. $1+x^3+x^6$

Q. Factorize: $a^2{b}^2+8ab-9$

1. $(ab-1)(ab+9)$
2. $(ab-9)(ab+1)$
3. $(ab+1)(ab+9)$
4. $(ab-9)(ab+9)$

Q. Akash has $6xy+4x{y}^2$ chocolates. He wants to distribute them to 2x children. How many chocolates does each of the child get if y = 2?

1. 12
2. 13
3. 15
4. 14

Q. Factorise $10000-x^4$ is ____

1. $(10-x)(x+10)(x^2+100)$
2. $(10-2x)(2x+10)(x^2+100)$
3. $(x-99)(x+99)(2x^2+100)$
4. $(x-100)(x+100)(x^2+99)$

Q. Factorize: $x(6x-5y)-4(6x-5y{)}^2$

1. $(6x+5y)(20y+23x)$
2. $(6x-5y)(20y-23x)$
3. $(6x-5y)(20y+23x)$
4. $(6x-5y)(20y-23x)$

Q.

Factorise $4a^{2}b-12a^2-16b+48$

1. 4xyz

2. 4xz

3. 4xy

4. 4xz

Q. Factorize: $a^4-2a^3-4a+8$

1. $(a-2)(a^2-4)$
2. $(a-2)(a^3-4)$
3. $(a-2)(a^3+4)$
4. $(a+2)(a^3-4)$

Q. Factorise the following trinomials:
$\frac{x^2}{4y^2}-\frac{1}{3}+\frac{y^2}{9x^2}$

Q. The expression $a^4-2a^3-4a+8$ can be factorise as

1. $(a^3+4)(a-2)$
2. $(a^3-4)(a+2)$
3. $(a^3+4)(a+2)$
4. $(a^3-4)(a-2)$

Q. The factorisation of $ab-2b+a^2-2a$ is equal to

1. (a + 2)(b + a)
2. (a - 2)(b - a)
3. (a - 2)(b + a)
4. (a +2)(b - a)

Q. Factorize $a^{5}b-a{b}^5$.

1. $ab(a^2+b^2)$
   
2. $(a+b)(a-b)$
   
3. $ab(a^2+b^2)(a+b)(a-b)$
4. $(a-b)(a^2+b^2)$
   

Q. Find the value of $\frac{x(y+2)}{x}$ if y = 2.

1. 2
2. 3
3. 4
4. 1

Q. Find the value of 𝒌 for which (𝒙 + 𝟐) is a factor of $f\left(x\right)=(x+1{)}^7+(2x+k{)}^3$.

Q. The factorisation of $2(x+y{)}^2-6(x+y)$ is

1. 2(x-y)(x+y-3)
2. 2(x+y)(x-y-3)
3. 2(x+y)(x+y+3)
4. 2(x+y)(x+y-3)

Q. Match the expression with their factorized form.

1. (a+1)(a+x)
2. (b+2)(b+y)
3. $ax(a+x)$
4. $axy(x+y)$

Q. Which of the following can be the factor(s) of $(a^2+\frac{1}{a^2}-2-3a+\frac{3}{a})$ ?

1. $(\frac{1}{a}-a)\left[\right(\frac{1}{a}-a)+3]$
2. $(a+\frac{1}{a})\left[\right(a+\frac{1}{a})-3]$
3. $(a-\frac{1}{a})\left[\right(a-\frac{1}{a})-3]$
4. $(a+\frac{1}{a})\left[\right(a-\frac{1}{a})+3]$

Q. Factorize: $x^2-3ax-88a^2$

1. $(x+11a)(x+8a)$
2. $(x-11a)(x-8a)$
3. $(x+11a)(x-8a)$
4. $(x-11a)(x+8a)$

Q. Find the value of $\frac{x(y+2)}{x}$ if y = 2.

1. 2
2. 4
3. 8
4. 16

Q. Factorize: $5x{y}^2+35xy$

1. $5xy(y+7)$
2. $5xy(y+7x)$
3. $5xy(x+7y)$
4. $xy(2y+35)$

Q. Akash has $6xy+4x{y}^2$ chocolates. He wants to distribute them to 2x children. How many chocolates does each of the child get if y = 2?

1. 12
2. 14
3. 18
4. 24