FACTORING EXPRESSIONS WORKSHEET

Factoring Expressions Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice problems on factoring algebraic expressions. 

Before we look at the worksheet, if you would like to learn how to factor algebraic expressions, 

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Factoring Expressions Worksheet - Problems

Problem 1 : 

Factor :

4x + 8

Problem 2 : 

Factor :

2x + 4y + 6z

Problem 3 : 

Factor :

16a + 64b - 4c

Problem 4 : 

Factor :

5x² - 15x

Problem 5 : 

Factor :

15x⁵ - 25x⁴ + 5x²

Factoring Expressions Worksheet - Solutions

Problem 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

8 / 4  =  2

Step 3 :

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

4(x + 2)

So,

4x + 8  =  4(x + 2)

Justify and Evaluate :

To verify our answer, let us use distributive property to multiply 4 and (x+2). 

Distribute 4 to x and 2. 

4(x + 2)  =  4 ⋅ x + 4 ⋅ 2

4(x + 2)  =  4x + 8

When we multiply 4 and (x + 2), we get the expression given.

So, 4 and (x + 2) are the factors of 4x + 8.

Problem 2 : 

Factor :

2x + 4y + 6z

Solution : 

Step 1 : 

Find the largest common divisors for 2x, 4y and 6z. 

The largest common divisor for 2x, 4y and 8z is 2. 

Step 2 :

Divide 2x, 4y and 8z by 2.

2x / 2  =  x

4y / 2  =  2y

6z / 2  =  3z

Step 3 :

Write the quotients x, 2y and 3z inside the parentheses and multiply by the largest common divisor 2.

2(x + 2y + 3z)

So,

2x + 4y + 6z  =  2(x + 2y + 3z)

Justify and Evaluate :

To verify our answer, let us use distributive property to multiply 2 and (x + 2y + 3z). 

Distribute 2 to x, 2y and 3z. 

2(x + 2y + 3z)  =  2 ⋅ x + 2 ⋅ 2y + 2 ⋅ 3z

2(x + 2y + 3z)  =  2x + 4y + 6z

When we multiply 2 and (x + 2y + 3z), we get the expression given.

So, 2 and (x + 2y + 3z) are the factors of 2x + 4y + 6z.

Problem 3 : 

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

4c / 4  =  c

Step 3 :

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

4(4a + 16b - c)

So, 

16a + 64b - 4c  =  4(4a + 16b - c) 

Justify and Evaluate :

To verify our answer, let us use distributive property to multiply 4 and (4a + 16b - c). 

Distribute 4 to 4a, 16b and c. 

4(4a + 16b - c)  =  4 ⋅ 4a + 4 ⋅ 16b - 4 ⋅ c

4(4a + 16b - c)  =  16a + 64b - 4c

When we multiply 4 and (4a+16b-c), we get the expression given.

So, 4 and (4a+16b-c) are the factors of 16a + 64b - 4c.

Problem 4 : 

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

15x / 5x   =  3

Step 3 :

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

(5x)(x - 3)

So,

5x² + 15x  =  (5x)(x - 3)

Justify and Evaluate :

To verify our answer, let us use distributive property to multiply 5x and (x - 3). 

Distribute 5x to x and 3. 

(5x)(x - 3)  =  5x ⋅ x - 5x ⋅ 3

(5x)(x - 3)  =  5x² - 15x

When we multiply 5x and (x - 3), we get the expression given.

So, 5x and (x - 3) are the factors of  5x² - 15x.

Problem 5 : 

Factor :

15x⁵ - 25x⁴ + 5x²

Solution : 

Step 1 : 

Find the largest common divisors for 15x⁵, -25x⁴ and 5x².

The largest common divisor for 15x⁵, -25x⁴ and 5x² is 5x². 

Step 2 :

Divide 15x⁵, -25x⁴ and 5x² by 5x².

15x⁵ / 5x²  =  3x³

-25x⁴ / 5x²  =  -5x²

5x⁵ / 5x²  =  1

Step 3 :

Write the quotients 3x³, -5x², and 1 inside the parentheses and multiply by the largest common divisor 5x².

5x²(3x³ - 5x² + 1)

So,

15x⁵ - 25x⁴ + 5x²  =  5x²(3x³ - 5x² + 1)

Justify and Evaluate :

To verify our answer, let us use distributive property to multiply 5x² and (3x³ - 5x² + 1).

Distribute 5x² to 3x³, -5x² and 1. 

5x²(3x³ - 5x² + 1)  =  5x² ⋅ 3x³ - 5x² ⋅ 5x² + 5x² ⋅ 1

5x²(3x³ - 5x² + 1)  =  15x⁵- 25x⁴ + 5x²

When we multiply 5x² and (3x³ - 5x² + 1), we get the expression given.

So, 5x² and (3x³ - 5x² + 1) are the factors of  15x⁵ - 25x⁴ + 5x².

After having gone through the stuff given above, we hope that the students would have understood how to factor algebraic expressions.

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