Method of Common Factors

Q.

Factorize the following using appropriate identities: $4y^2-4y+1$.

Q.

Factorize:

$a^4-5a^2-36$

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

2. $(a^2+9)(a^2+4)$

3. $(a-9)(a+4)$

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

Q.

One of the factors of $x^2-2x-15$ is _____.

1. x-3

2. x+5

3. x - 15

4. x+3

Q.

$\text{Which of the following represents the}\text{factorisation of}2xy+6y^2?$

1. $2y(x+3y)$

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

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

4. $6y(x+y)$

Q.

Factor it completely $7x^2-31x-20$:

Q.

Factorisation of $81x^3-x{y}^2$ gives

1. $x(9x-y)(9x+y)$

2. $x(9x-y)(9x-1)$

3. $x^2(9x+y)$

4. $x(9y-x)(9x+y)$

Q. Factorize the expression and divide them as directed:
$(2x^3-12x^2+16x)÷(x-2)(x-4)$

Q.

What are the common factors of ​$3x^{3}y,5x{y}^2$ and $15xy$?

1. $x,y,xy,x{y}^2,x^{3}y$

2. $x,y,xy,x^{2}y$

3. $x,y,xy$

4. $xy,x^{2}y,x{y}^2$

Q.

Factorise $m^2+7m-60-16n^2$

1. $(m+3-4n)(m+3-4n)$

2. $(m+3+4n)(m+3-4n)$

3. $(m-3+4n)(m-3-4n)$

4. $(m+2+4n)(m+2-4n)$

Q.

Factor(s) of $a^2-2ab+b^2-c^2$ is/are​

1. a-b+c

2. a-b-c

3. Both 1 and 2

4. None of the above

Q. Factorise $6xy-4y+6-9x$.

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

Q.

Factorise $a^2+7a+10$ + pa + 5p

1. (a+5) + (a+ 2+ p)

2. (a+5) + (a+ p)

3. (a+2) + (a+ 5+ p)

4. (a+7+ p) + (a+ p)

Q. $12ab+9a+12+16b=$

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

Q.

Factorisation of $a^2+7a+10$ gives:

1. 1

2. a+1

3. a+5

4. a+2

Q.

$10lm$ is one of the factors of $20l^{2}m+30alm$.
The other factor is

1. $5l+3m$

2. $3l+2a$

3. $2l+3a$

4. $3l+2m$

Q. Factorise : $2a+6b-3(a+3b{)}^2$
$2a+6b-3(a+3b{)}^2$
$=2(a+3b)-3(a+3b{)}^2[Taking2commonfrom2a+6b]$
$=(a+3b)\left\{\begin{array}{c}2-3(a+3b)\end{array}\right\}\left[Taking\right(a+3b\left)common\right]$
$=(a+3b)(2-3a-9b)$

Q. Factorise: 3a${}^2$ + 5ab + 2b${}^2$
(2 marks)

Q.

Factorise $a^2-81(b-c{)}^2$

1. (a+ 81b- 81c)(a-81b-81c)

2. (a+ 9b- 9c)(a-9b-9c)

3. (a+ 9b+9c)(a-9b-9c)

4. (a-b+c)(a-b-c)

Q.

Factorize:

$25(a-5b{)}^2-4(a-3b{)}^2$

1. $(3a-19b).(7a+31b)$

2. $(7a-19b).(3a-31b)$

3. $(3a+19b).(7a+31b)$

4. $(3a-19b).(7a-31b)$

Q.

Which of the following is one of the factors of

$(x^4+x^2-20)$

1. $(x^2+4)$

2. $(x-4)$

3. $(x^2+5)$

4. $(x^2-5)$

Q.

Which of the following are the factors of

$x^2+4(x-3)$

1. (x + 6)

2. (x - 6)

3. (x + 2)

4. (x - 2)

Q.

The possible expressions for the adjacent sides of the rectangle having

$35y^2+13y-12$ as its area are ____ and ____

1. (5y−4) and (7y+3)

2. (5y+4) and (7y−3)

3. (5y−4) and (7y−3)

4. (5y+4) and (7y+3)

Q.

$(x+4{)}^2-5xy-20y-6y^2=$

1. (x−6y+4)(x+y+4)

2. (x+6y+4)(x+y+4)

3. (x−6y+4)(x−y−4)

4. (x−6y+4)(x−y+4)

Q.

Factors of $a^2-b^2-4ac+4c^2$ are

$(a-2c+b)$ and $(a+2c-b)$

1. True

2. False

Q.

Factorize completely :

$x^2-16y^2-2x-8y$

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

2. $(x+4y)(x+4y-2)$

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

4. $(x+4y)(x-4y+2)$

Q. Factorise: $x^3{y}^3-7^3$

a. (xy-7)($x^2{y}^2+7xy+49$)
b. (xy-7)($x^2{y}^2-7xy+49$)
c. (xy+7)($x^2{y}^2+7xy+49$)
d. (xy+7)($x^2{y}^2-7xy+49$)
$\left[1\right]$

Q.

Factorize $2x^6+12x^2$

1. $2x^2(x^4+6)$

2. $2x(x^4+6)$

3. $2x^2(x^2+6)$

4. $2x^2(x^3+6)$

Q.

Factor the expression using GCF.

$9-5x$

Q.

Factorize: (a^2 - ab - 3a + 3b)

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

2. (a + b)(a + 3)

3. (a - b)(a - 3)

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

Q.

Factorize:

$a^2-b^2-2b-1$

1. $[a-b-1][a-b-1]$

2. $[a-b-1][a+b+1]$

3. $[a+b+1][a-b+1]$

4. $[a-b+1][a+b-1]$