The problem requires us to factor three linear expressions by filling in the blanks with appropriate numbers. The expressions are: $72x - 27$ $42x + 54$ $24x - 30xy$

1. Problem Description

The problem requires us to factor three linear expressions by filling in the blanks with appropriate numbers.

The expressions are:

$72x - 27$

$42x + 54$

$24x - 30xy$

2. Solution Steps

For the first expression, $72x - 27$:

We need to find the greatest common divisor (GCD) of 72 and

2

7. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and

7

2. The factors of 27 are 1, 3, 9, and

2

7. The GCD of 72 and 27 is

9. Therefore, we can factor out

9. $72x - 27 = 9(8x - 3)$

The blanks should be filled with 9, 8, and

3.

For the second expression, $42x + 54$:

We need to find the greatest common divisor (GCD) of 42 and

5

4. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and

4

2. The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and

5

4. The GCD of 42 and 54 is

6. Therefore, we can factor out

6. $42x + 54 = 6(7x + 9)$

The blanks should be filled with 6, 7, and

9.

For the third expression, $24x - 30xy$:

We need to find the greatest common divisor (GCD) of 24 and

3

0. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and

2

4. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and

3

0. The GCD of 24 and 30 is

6. We also see that $x$ is a common factor. Therefore, we can factor out $6x$.

$24x - 30xy = 6x(4 - 5y)$

The blanks should be filled with 6, 4, and

5.

3. Final Answer

$72x - 27 = 9(8x - 3)$

$42x + 54 = 6(7x + 9)$

$24x - 30xy = 6x(4 - 5y)$