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

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