# 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,

## 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 - 25x+ 5x2

Solution :

Step 1 :

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

The largest common divisor for 15x5, -25xand 5xis 5x2

Step 2 :

Divide 15x5, -25xand 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 - 25x+ 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 5xto 3x3, -5xand 1.

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

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