2. Susan incorrectly factored the expression below. $$ \begin{array}{l}12 a-15 b+6 \ 3(4 a+5 b+3)\end{array} $$ a. Explain any errors Susan may have made when factoring. Factor the expression correctly.

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To analyze Susan's factoring of the expression $$ 12a - 15b + 6 $$ and identify any errors, let's break down the steps involved in factoring the expression correctly.

### Step 1: Identify the common factors

The expression $$ 12a - 15b + 6 $$ consists of three terms: $$ 12a $$, $$ -15b $$, and $$ 6 $$. We need to find the greatest common factor (GCF) of these terms.

- The coefficients are $$ 12 $$, $$ -15 $$, and $$ 6 $$.
- The GCF of $$ 12 $$, $$ 15 $$, and $$ 6 $$ is $$ 3 $$.

### Step 2: Factor out the GCF

Now, we can factor out the GCF $$ 3 $$ from each term in the expression:

$$
12a - 15b + 6 = 3(4a - 5b + 2)
$$

### Step 3: Compare with Susan's Factoring

Susan factored the expression as $$ 3(4a + 5b + 3) $$. The errors in her factoring are:

1. **Incorrect signs**: She used $$ +5b $$ instead of $$ -5b $$ for the second term.
2. **Incorrect constant**: She used $$ +3 $$ instead of $$ +2 $$ for the constant term.

### Conclusion

The correct factorization of the expression $$ 12a - 15b + 6 $$ is:

$$
3(4a - 5b + 2)
$$

This shows that Susan made errors in both the signs and the constant term during her factoring process.
Susan incorrectly factored the expression by using the wrong signs and a different constant term. The correct factorization is $$ 3(4a - 5b + 2) $$.

2. Susan incorrectly factored the expression below. \[ \begin{array}{l}12 a-15 b+6 \\ 3(4 a+5 b+3)\end{array} \] a. Explain any errors Susan may have made when factoring. Factor the expression correctly.

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