\begin{tabular}{l|l} Directions: Factor each polynomial. \\ \hline 1. \( x^{3}+x^{2}+2 x+2 \) & 2. \\ \hline\end{tabular}

Factor the expression by following steps: - step0: Factor: \(x^{3}+x^{2}+2x+2\) - step1: Calculate: \(x^{3}+2x+x^{2}+2\) - step2: Rewrite the expression: \(x\times x^{2}+x\times 2+x^{2}+2\) - step3: Factor the expression: \(x\left(x^{2}+2\right)+x^{2}+2\) - step4: Factor the expression: \(\left(x+1\right)\left(x^{2}+2\right)\) Let's factor the polynomial \( x^{3}+x^{2}+2x+2 \) step by step. 1. **Group the terms**: We can group the polynomial into two parts: \[ (x^{3} + x^{2}) + (2x + 2) \] 2. **Factor out common factors from each group**: - From the first group \( x^{3} + x^{2} \), we can factor out \( x^{2} \): \[ x^{2}(x + 1) \] - From the second group \( 2x + 2 \), we can factor out \( 2 \): \[ 2(x + 1) \] 3. **Combine the factored groups**: Now we can combine the factored terms: \[ x^{2}(x + 1) + 2(x + 1) \] 4. **Factor out the common binomial factor \( (x + 1) \)**: \[ (x + 1)(x^{2} + 2) \] Thus, the factored form of the polynomial \( x^{3}+x^{2}+2x+2 \) is: \[ (x + 1)(x^{2} + 2) \] For the second polynomial, it seems there was an error in the input provided ("2."). If you have another polynomial to factor, please provide it, and I will assist you with that as well!