Factorization by Taking Common Factor

Q. Josh is trying to factorize the polynomial, $2x^2-13x+21$ by splitting the middle term ($-13x$). Which of the following ways should he split the middle term such that the factorization is possible?

1. $2x^2-3x-7x+21$
2. $2x^2-6x-7x+21$
3. $2x^2-14x-2x+21$
4. $2x^2+7x-6x+21$

Q. Which of the following is not a factor of 15?

1. 1
2. 3
3. 6
4. 15

Q. Question 2(ii)
Factorise the following expressions
$6p-12q$

Q. Question 1(ii)
Find the common factors of the given terms.
$2y,22xy$

Q. Factorise the expression:
$z-7+7xy-xyz.$

1. $(z+7)(1+xy)$
2. $(z-7)(1+xy)$
3. $(x+7)(1-zy)$
4. $(z-7)(1-xy)$

Q. $22+77x$ can be written as.

1. $22(1+7x)$
2. $11(2+7x)$
3. $2(11+77x)$

Q. Josh is trying to factorize the polynomial, $2x^2-13x+21$ by splitting the middle term ($-13x$). Which of the following ways should he split the middle term such that the factorization is possible?

1. $2x^2-3x-7x+21$
2. $2x^2-6x-7x+21$
3. $2x^2-14x-2x+21$
4. $2x^2+7x-6x+21$

Q. $Factorise:m^2-4m-m+4$

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

Q. The factorisation of 24xy + 8yz is

1. 24y(3x+z)
2. 3y(8x+z)
3. 8y(3x+z)
4. 8z(3x+y)

Q. Question 27

The factorised form of $3x-24$ is
a) $3x\times 24$
b) $3(x-8)$
c) $24(x-3)$
d) $3(x-12)$

Q.

Factor the expression using GCF.

$2b+8$

Q. Find the common factor of $10PQ,20QR\text{and}30RP.$

1. $5$
2. $10$
3. $5P$
4. $5Q$

Q.

Common factors of the first two terms in the expression 5xy + 4ax + 6pa + 8px are:

1. x, y, a

2. 5, x, y, 4, a

3. x

4. y, a

Q. Which of the following is the factorisation of (4xy + 8x)?

1. 4(xy + 2)
2. 4x(y + 2)
3. 8x(y + 1)
4. 8x(x + y)

Q. $\text{Factorise the expression:}-16y^{2}z+20z^3$

1. $4z(y^2+5z^2)$
2. $4z(-4y^2-5z^2)$
3. $4z(-4y^2+5z^2)$
4. $4z(4y^2+5z^2)$

Q. Which of the following is one of the common factors of 48 and 24?

1. 11
2. 16
3. 5
4. 4

Q. $\text{Factorise:}12xy-8x+9y-6$

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

Q. $\text{Find the factors of}(ax+by+bx+az+ay+bz).$

1. $(a+b),(2x+2y+2z)$
2. $(bxc+ay),(ax+by)$
3. $(x+y+z),(a+b)$
4. $(bc+axy),(a+by)$

Q. $\text{Factorise the expression:}2xy+3x+2y+3.$

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

Q.

Which of the following is the factorised form of $20l^{2}m+30alm?$

1. $10lm(l+3a)$
2. $10lm(2l+3a)$
3. $5lm(2l+3a)$
4. $10lm(2l-3a)$

Q. Which of the following is the common factor of 4ab, 6bc and 8abc?

1. 2c
2. 4b
3. 2b
4. 3a

Q. Find all the factors of 148.

1. 1, 2, 4, 37
2. 2 and 4
3. 2, 4, 37, 74
4. 1, 2, 4, 37, 74, 148