# FACTORING LINEAR EXPRESSIONS PRACTICE

## About "Factoring linear expressions practice"

Factoring linear expressions practice :

Here we are going to see some practice questions on factoring linear expressions.

## How to factor linear expressions ?

Factoring (called "Factorising" in the UK) is the process of finding the factors.

It is like "splitting" an expression into a multiplication of simpler expressions.

Factoring linear expressions - Steps

Step 1 :

Find the largest common divisor for all the terms in the expression

Step 2 :

Divide each term of the expression by the largest common divisor.

Step 3:

Write the quotients inside the parenthesis.

Step 4 :

Write the largest common divisor and the parenthesis together using multiplication.

## Factoring linear expressions practice questions

(1)  Factor : 4x + 8

(2) Factor : 16a + 64b - 4c

(3)  Factor : 36x - 16

(4)  Factor : 35 + 21 a

(5)  Factor : 4a - 8b + 5ax - 10bx

Question 1 :

Factor : 4x + 8

Solution :

Step 1 :

Find the largest common divisors for 4x and 8.

The largest common divisor for 4x and 8 is 4.

Step 2 :

Divide 4x and 8 by 4

4x / 4  =  x and 8 / 4  =  2

Step 3 :

Write the quotients x and 2 inside the parenthesis and multiply by the largest common divisor 4.

4(x + 2)

Hence, 4x + 8  =  4(x + 2)

Question 2 :

Factor : 16a + 64b - 4c

Solution :

Step 1 :

Find the largest common divisors for 16a, 64b and 4c.

The largest common divisor for  16a, 64b and 4c is 4.

Step 2 :

Divide 16a, 64b and 4c by 4

16a / 4  =  4a, 64b / 4  =  16b and 4c / 4  =  c

Step 3 :

Write the quotients 4a, 16b and c inside the parenthesis and multiply by the largest common divisor 4.

4(4a + 16b - c)

Hence, 16a + 64b - 4c  =  4(4a + 16b - c)

Question 3 :

Factor : 36x - 16

Solution :

Step 1 :

Find the largest common divisors for 36x and 16.

The largest common divisor for 36x and 16 is 4.

Step 2 :

Divide 36x and - 16 by 4.

36x / 4  =  9x and -16 / 4   =  -4

Step 3 :

Write the quotients 9x and -4 inside the parenthesis and multiply by the largest common divisor 4.

4(9x - 4)

Hence, 36x - 16  =  4(9x - 4)

Question 4 :

Factor : 35 + 21 a

Solution :

Step 1 :

Find the largest common divisors for 35 and 21a.

The largest common divisor for 35 and 21a is 7.

Step 2 :

Divide each term by 7

35 / 7  =  5, 21a / 7   =  3a

Step 3 :

Write the quotients 5 and 3a inside the parenthesis and multiply by the largest common divisor 7.

7 (5 + 3a)

Hence, 35 + 21a  =  7 (5 + 3a)

Question 5 :

Factor : 4a - 8b + 5ax - 10bx

Solution :

Step 1 :

Since we have four terms, we can group them into two terms

=  4a - 8b + 5ax - 10bx

Common divisor for first two terms, that is 4a and 8b is 4

Common divisor for third and fourth terms, that is 5ax and 10bx is 5x.

Step 2 :

Divide first two terms by 4

4a/4  =  1a

- 8b/4  =  -2b

Divide third and fourth terms by 5x

5ax/5x  =  a

- 10bx/5x  =  -2b

Step 3 :

=  4(a - 2b) + 5x (a - 2b)

=  (a - 2b) (4 + 5x) After having gone through the stuff given above, we hope that the students would have understood "Factoring linear expressions practice".

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