FACTORS OF LINEAR EXPRESSIONS

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

It is like "splitting" an expression as a product of simpler expressions.

The following steps would be useful to factor algebraic expressions. 

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 : 

Find the largest common divisors for 4x and 8. 

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

Divide 4x and 8 by 4

4x/4  =  x

8/4  =  2

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

4(x + 2)

So, 

4x + 8  =  4(x + 2)

Example 2 : 

Factor :

16a + 64b - 4c

Solution : 

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

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

Divide 16a, 64b and 4c by 4 

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

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

4(4a + 16b - c)

So,

16a + 64b - 4c  =  4(4a + 16b - c) 

Example 3 : 

Factor :

-25x + 15

Solution : 

Find the largest common divisors for 25x and 15. 

The largest common divisor for 25x and 15 is 5. 

Divide 25x and 15 by 5.

25x/5  =  5x

15/5   =  3

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

5(-5x + 3)

So,

-25x + 15  =  5(-5x + 3)

Example 4 : 

Factor :

1.5y - 9

Solution : 

Find the largest common divisors for 1.5y and  9.

The largest common divisor for 1.5y and 9. is 1.5

Divide each term by 1.5y.

1.5y/1.5  =  y 

9/1.5  =  6

Write the quotients y and 6 inside the parenthesis and multiply by the largest common divisor 1.5.

1.5(y - 6)

So, 

1.5y - 9  =  1.5(y - 6)

Example 5 : 

Factor : 

4w - 8x + 16y - 32z

Solution : 

Find the largest common divisors for 4w, 8x, 16y and 32z.

The largest common divisor 4w, 8x, 16y and 32z is 4.

Divide each term by 4.

4w/4  =  w

8x/4  =  2x

16y/4  =  4y

32z/4  =  8z

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

4(w - 2x + 4y - 8z)

So, 

4w - 8x + 16y - 32z  =  4(w - 2x + 4y - 8z)

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