FACTORS OF  LINEAR EXPRESSIONS

About "Factors of linear expressions"

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. 

Factors of linear expressions - Examples

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.

You can also visit the following web pages on different stuff in math. 

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

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

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6