## Exercise 14 A

**Factorize completely by removing a monomial factor.**

Question 1

**3y – 9**

Sol :

= 3(y) + 3( -3)

The common factor is 3 , dividing each term by 3 we obtain other factor ( y – 3 )

= 3(y-3)

Question 12

** 5x + 10**

Sol :

= 5(x) + 5( 2)

The common factor is 5 , dividing each term by 3 we obtain other factor ( x + 2 )

= 5(x + 2)

Question 3

**2x – 4**

Sol :

= 2( x) + 2( -2 )

The common factor is 2 , dividing each term by 2 we obtain other factor ( x – 2 )

= 2( x – 2 )

Question 4

**5m + 5n**

Sol :

= 5( m ) + 5( n )

The common factor is 5 , dividing each term by 5 we obtain other factor ( m + n )

= 5( m + n )

Question 5

**4a + 8b**

Sol :

= 4( a ) + 4( 2b )

The common factor is 4 , dividing each term by 4 we obtain other factor ( a + 2b )

= 4( a + 2b )

Question 6

**7x – 14y**

Sol :

= 7( x ) + 7(-2y )

The common factor is 7 , dividing each term by 7 we obtain other factor ( x – 2y )

= 7( x – 2y )

Question 7

** -3m – 15n**

Sol :

= -3( m )+ {-3( 5n )]

The common factor is -3 , dividing each term by -3 we obtain other factor ( m + 5n )

= -3( m + 5n )

Question 8

**-7p – 14q**

Sol :

= -7( p ) + {-7( 2q )}

The common factor is -7 , dividing each term by -7 we obtain other factor ( p + 2q )

= -7( p + 2q )

Question 9

**6x ^{2} – 11x**

Sol :

= x(6x) – x(11)

The common factor is x , dividing each term by x we obtain other factor (6x-11)

= x(6x-11)

Question 10

**3y ^{2} – 7y**

Sol :

= y( 3y ) – y( 7 )

The common factor is y , dividing each term by y we obtain other factor ( 3y – 7 )

= y( 3y – 7 )

Question 11

**ax + bx**

Sol :

= x( a ) + x( b )

The common factor is x , dividing each term by x we obtain other factor ( a + b )

= x( a + b )

Question 12

**x ^{2}y + xy^{2}**

Sol :

= x(xy) + (xy)y

The common factor is xy , dividing each term by xy we obtain other factor ( x + y )

= xy( x + y )

Question 13

**4 + 12x ^{2}**

Sol :

= 4( 1 ) + 4( 3x^{2 })

The common factor is 4 , dividing each term by 4 we obtain other factor ( 1 + 3x^{2 })

= 4( 1 + 3x^{2 })

Question 14

**ax + ay + az**

Sol :

= a( x ) + a( y ) + a( z )

The common factor is a , dividing each term by a we obtain other factor ( x + y + z )

= a( x + y + z )

Question 15

**a ^{3}b + ab^{3}**

Sol :

= a^{2}(ab) + (ab)b^{2}

The common factor is ab , dividing each term by ab we obtain other factor (a^{2} + b^{2})

= ab(a^{2} + b^{2})

Question 16

**x ^{2}y^{2} + x^{2}**

Sol :

= x^{2}(y^{2})+ x^{2}(1)

The common factor is x^{2} , dividing each term by x^{2} we obtain other factor (y^{2}+1)

= x^{2}(y^{2}+1)

Question 17

**p ^{2} – 3pq +pq^{2}**

Sol :

= p(p) – p(3q) +p(q^{2})

The common factor is p , dividing each term by p we obtain other factor (p-3q+q^{2})

= p(p-3q+q^{2})

Question 18

**7y ^{3} – 5y^{2}**

Sol :

= (7y)y^{2} – (5)y^{2}

The common factor is y , dividing each term by y we obtain other factor ( 7y – 5 )

= y^{2}( 7y – 5 )

Question 19

**6x ^{3} -10x^{2}**

Sol :

= 2x^{2}(3x) – 2x^{2}(5)

The common factor is 2x^{2} , dividing each term by 2x^{2} we obtain other factor ( 3x – 5 )

= 2x^{2}( 3x – 5 )

Question 20

**2ab ^{2} – 6bc + 6abc**

Sol :

= 2b(ab) – 2b(3c) + 2b(4ac)

The common factor is 2b , dividing each term by 2b we obtain other factor ( ab – 3c + 4ac )

= 2b( ab – 3c + 4ac )

Question 21

**12p ^{5} + 16p^{4} – 20p^{3}**

Sol :

= 4p^{3}(3p^{2})+ 4p^{3}(4p) – 4p^{3}(5)

The common factor is 4p^{3} , dividing each term by 4p^{3} we obtain other factor ( 3p^{2} + 4p – 5 )

= 4p^{3}( 3p^{2} + 4p – 5 )