Question 7 of 8, Step 1 of 1 Completely factor the expression by grouping, if possible. correct \( 3 a^{2}-6+a^{2} x+3 x \)

To factor the expression \( 3a^{2} - 6 + a^{2}x + 3x \) by grouping, we will follow these steps: 1. **Rearrange the expression**: Group the terms in pairs that can be factored together. \[ (3a^{2} + a^{2}x) + (-6 + 3x) \] 2. **Factor out the common factors from each group**: - From the first group \( 3a^{2} + a^{2}x \), we can factor out \( a^{2} \): \[ a^{2}(3 + x) \] - From the second group \( -6 + 3x \), we can factor out \( -3 \): \[ -3(2 - x) \] 3. **Rewrite the expression**: Now we have: \[ a^{2}(3 + x) - 3(2 - x) \] 4. **Check for a common binomial factor**: Notice that \( 3 + x \) can be rewritten as \( -(2 - x) \): \[ a^{2}(3 + x) + 3(3 + x) \] 5. **Factor out the common binomial factor \( (3 + x) \)**: \[ (3 + x)(a^{2} + 3) \] Thus, the completely factored form of the expression \( 3a^{2} - 6 + a^{2}x + 3x \) is: \[ (3 + x)(a^{2} + 3) \]