(e) 3x2 + 10x + 3 by x + 3
​

(3x+1)(x+3) is the factorised form for the expression.

Step-by-step explanation:

:3

x

2

+

10

x

+

3

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like  

a

x

2

+

b

x

+

c

, we need to think of 2 numbers such that:

N

1

⋅

N

2

=

a

⋅

c

=

3

⋅

3

=

9

and,

N

1

+

N

2

=

b

=

10

After trying out a few numbers we get:

N

1

=

9

and  

N

2

=

1

9

⋅

1

=

9

, and  

9

+

(

1

)

=

10

3

x

2

+

10

x

+

3

=

3

x

2

+

9

x

+

1

x

+

3

=

3

x

(

x

+

3

)

+

1

(

x

+

3

)

(

3

x

+

1

)

(

x

+

3

)

is the factorised form for the expression.

is the factorised form for the expression.