FACTORING LINEAR EXPRESSIONS PRACTICE

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)

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

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)

Example 3 :

Factor :

36x - 16

Solution : 

Find the largest common divisors for 36x and 16. 

The largest common divisor for 36x and 16 is 4.

Divide 36x and - 16 by 4.

36x/4  =  9x

-16/4  =  -4

Write the quotients 9x and -4 inside the parenthesis and multiply by the largest common divisor 4.

4(9x - 4)

Example 4 :

Factor :

35 + 21a

Solution : 

Find the largest common divisors for 35 and 21a.

The largest common divisor for 35 and 21a is 7.

Divide each term by 7

35/7  =  5

21a/7  =  3a

Write the quotients 5 and 3a inside the parenthesis and multiply by the largest common divisor 7.

7(5 + 3a)

So, 

35 + 21a  =  7(5 + 3a)

Example 5 :

Factor : 

4a - 8b + 5ax - 10bx

Solution : 

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.

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

So, 

=  4(a - 2b) + 5x (a - 2b)

=  (a - 2b) (4 + 5x)

Example 6 :

Factor : 

x² + 2x + xy + 2y

Solution : 

Since we have four terms, we can use grouping method to factor this.

= x² + 2x + xy + 2y

Factoring x from the first two terms and factoring y from 3rd and 4th terms, we get 

= x (x + 2) + y(x + 2)

= (x + y)(x + 2)

So, the factors are (x + y) and (x + 2).

Example 7 :

Factor : 

6xy + 10x² y

Solution : 

Since we have four terms, we can use grouping method to factors.

= 6xy + 10x² y

Factoring 2xy, we get

= 2xy(3 + 5x)

So, the factors are 2xy and (3 + 5x)

Example 8 : 

Factor : 

n² + 2n + 3mn + 6m

Solution : 

Since we have four terms, we can use grouping method to factors.

= n² + 2n + 3mn + 6m

Factoring n from first two terms and factoring 3m from 3rd and 4th terms, we get

= n(n + 2) + 3m(n + 2)

= (n + 3m) (n + 2)

So, the factors are (n + 3m) and (n + 2)

Example 9 :

Factor : 

x² + 5x + 2x + 10

Solution : 

Since we have four terms, we can use grouping method to factors.

= x² + 5x + 2x + 10

Factoring x from first two terms and factoring 2 from 3rd and 4th terms, we get

= x(x + 5) + 2(x + 5)

= (x + 2)(x + 5)

So, the factors are (x + 2) and (x + 5)

Example 10 :

Factor : 

4u² + v + 2uv + 2u

Solution : 

Since we have four terms, we can use grouping method to factors.

= 4u² + v + 2uv + 2u

= 4u² + 2uv  + v + 2u

Factoring  2u from first two terms and factoring 1 from 3rd and 4th terms, we get

= 2u(2u + v) + 1(v + 2u)

= (2u + v)(v + 2u)

So, the factors are (2u + v) and (2u + v)

Example 11 :

Factor : 

x² a + x² b - 16a - 16b

Solution : 

Since we have four terms, we can use grouping method to factors.

= x² a + x² b - 16a - 16b

Factoring  x² from first two terms and factoring 16 from 3rd and 4th terms, we get

= x²(a + b) - 16(a + b)

= (x² - 16)(a + b)

= (x² - 4²)(a + b)

= (x + 4)(x - 4)(a + b)

So, the factors are (x + 4)(x - 4) and (a + b).

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.