The problem asks us to factor the given linear expressions. We have three expressions: $40x - 56$, $90x + 40$, and $12x - 18xy$. We need to find the greatest common factor (GCF) of the terms in each expression and factor it out.

1. Problem Description

The problem asks us to factor the given linear expressions. We have three expressions: $40x - 56$, $90x + 40$, and $12x - 18xy$. We need to find the greatest common factor (GCF) of the terms in each expression and factor it out.

2. Solution Steps

a) Factoring $40x - 56$:

The factors of 40 are 1, 2, 4, 5, 8, 10, 20,

4

0. The factors of 56 are 1, 2, 4, 7, 8, 14, 28,

5

6. The greatest common factor of 40 and 56 is

8. So, $40x - 56 = 8(5x - 7)$.

b) Factoring $90x + 40$:

The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45,

9

0. The factors of 40 are 1, 2, 4, 5, 8, 10, 20,

4

0. The greatest common factor of 90 and 40 is

1

0. So, $90x + 40 = 10(9x + 4)$.

c) Factoring $12x - 18xy$:

The factors of 12 are 1, 2, 3, 4, 6,

1

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

1

8. The greatest common factor of 12 and 18 is

6. Also both terms contain $x$.

So, we can factor out $6x$.

Then $12x - 18xy = 6x(2 - 3y)$.

3. Final Answer

$40x - 56 = 8(5x - 7)$

$90x + 40 = 10(9x + 4)$

$12x - 18xy = 6x(2 - 3y)$