**Factoring linear expressions practice :**

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

(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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