Factors of 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.

**Example 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)

**Example 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)

**Example 3 : **

Factor : 5x² - 15x

**Solution : **

**Step 1 : **

Find the largest common divisors for 5x² and 15x.

The largest common divisor for 5x² and 15x is 5x.

**Step 2 :**

Divide 5x² and 15x by 5x

5x² / 5x = x and 15x / 5x = 3

**Step 3 :**

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

(5x)(x - 3)

Hence, 5x² + 15x = (5x)(x - 3)

**Example 4 : **

Factor : 15y² - 9y + 6

**Solution : **

**Step 1 : **

Find the largest common divisors for 15y², - 9y and 6

The largest common divisor for 15y², - 9y and 6 is 3.

**Step 2 :**

Divide each term by 3

15y² / 3 = 5y², - 9y / 3 = -3y, 6 / 3 = 2

**Step 3 :**

Write the quotients 5y², -3y and 2 inside the parenthesis and multiply by the largest common divisor 3.

3 (5y² -3y + 2)

Hence, 15y² - 9y + 6 = 3 (5y² -3y +2)

**Example 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 "Factors of linear expressions".

Apart from the stuff given above, if you want to know more about "Factors of linear expressions", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**