The problem asks us to identify whether the coefficients of each given quadratic expression have a common factor greater than 1. If they do, we must "undistribute" that factor by factoring it out of the expression. The expressions are: $3x^2 + 15x - 12$ $8x^2 - 12x + 20$ $7x^2 + 161x - 36$

1. Problem Description

The problem asks us to identify whether the coefficients of each given quadratic expression have a common factor greater than

1. If they do, we must "undistribute" that factor by factoring it out of the expression. The expressions are:

$3x^2 + 15x - 12$

$8x^2 - 12x + 20$

$7x^2 + 161x - 36$

2. Solution Steps

For the first expression, $3x^2 + 15x - 12$, we look for a common factor of 3, 15, and -

1

2. The greatest common divisor of 3, 15, and 12 is

3. So, we can factor out

3. $3x^2 + 15x - 12 = 3(x^2 + 5x - 4)$

For the second expression, $8x^2 - 12x + 20$, we look for a common factor of 8, -12, and

2

0. The greatest common divisor of 8, 12, and 20 is

4. So, we can factor out

4. $8x^2 - 12x + 20 = 4(2x^2 - 3x + 5)$

For the third expression, $7x^2 + 161x - 36$, we look for a common factor of 7, 161, and -

3

6. 7 is a prime number. $161 = 7 \cdot 23$, and $36 = 2^2 \cdot 3^2$.

The greatest common divisor of 7, 161, and 36 is

1. So, there is no common factor other than

1. $7x^2 + 161x - 36$ remains unchanged.

3. Final Answer

$3x^2 + 15x - 12 = 3(x^2 + 5x - 4)$

$8x^2 - 12x + 20 = 4(2x^2 - 3x + 5)$

$7x^2 + 161x - 36$