`x^3+2x^2+5x+10`

Answer

To factor the polynomial \( x^3 + 2x^2 + 5x + 10 \), we can follow these steps:

### Step 1: Group the terms
We can group the polynomial into two parts:
\[ (x^3 + 2x^2) + (5x + 10) \]

### Step 2: Factor out the common terms from each group
From the first group \( x^3 + 2x^2 \), we can factor out \( x^2 \):
\[ x^2(x + 2) \]
From the second group \( 5x + 10 \), we can factor out \( 5 \):
\[ 5(x + 2) \]

### Step 3: Combine the factored groups
Now, we can write the polynomial as:
\[ x^2(x + 2) + 5(x + 2) \]

### Step 4: Factor out the common binomial factor
Notice that \( (x + 2) \) is a common factor:
\[ (x + 2)(x^2 + 5) \]

### Final Answer
Thus, the factorization of the polynomial \( x^3 + 2x^2 + 5x + 10 \) is:
\[ (x + 2)(x^2 + 5) \]

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