The problem requires us to factor linear expressions and fill in the blanks to complete the factored form. We have three expressions to factor: * $36xy - 24x$ * $16x + 28$ * $15 - 45x$

1. Problem Description

The problem requires us to factor linear expressions and fill in the blanks to complete the factored form. We have three expressions to factor:

* $36xy - 24x$

* $16x + 28$

* $15 - 45x$

2. Solution Steps

* For $36xy - 24x$:

* Find the greatest common factor (GCF) of $36xy$ and $24x$. The GCF of 36 and 24 is

1

2. Both terms contain the variable $x$, so the GCF is $12x$.

* Factor out $12x$ from each term: $36xy - 24x = 12x(3y - 2)$

* So, the blanks should be filled in as: $36xy - 24x = 12x(3y - 2)$

* For $16x + 28$:

* Find the GCF of $16x$ and $28$. The GCF of 16 and 28 is

4. * Factor out 4 from each term: $16x + 28 = 4(4x + 7)$

* So, the blanks should be filled in as: $16x + 28 = 4(4x + 7)$

* For $15 - 45x$:

* Find the GCF of $15$ and $45x$. The GCF of 15 and 45 is

1

5. * Factor out 15 from each term: $15 - 45x = 15(1 - 3x)$

* So, the blanks should be filled in as: $15 - 45x = 15(1 - 3x)$

3. Final Answer

* $36xy - 24x = 12x(3y - 2)$

* $16x + 28 = 4(4x + 7)$

* $15 - 45x = 15(1 - 3x)$