Factors of `x^2+7x+10` are
A. (x-5) (x-2)
B. (x+5) (x+2)
C. (x-5) (x+2)
D. (x-4) (x+2)

Options

A. B
B. C
C. D
D. A

Answer

To factor the quadratic expression \(x^2 + 7x + 10\), we will follow these steps:

### Step 1: Identify the coefficients
The expression is in the standard form \(ax^2 + bx + c\), where:
- \(a = 1\)
- \(b = 7\)
- \(c = 10\)

### Step 2: Find two numbers that multiply to \(c\) and add to \(b\)
We need to find two numbers that:
- Multiply to \(c = 10\)
- Add to \(b = 7\)

The pairs of factors of 10 are:
- \(1 \times 10\)
- \(2 \times 5\)

Now, checking their sums:
- \(1 + 10 = 11\) (not suitable)
- \(2 + 5 = 7\) (suitable)

Thus, the two numbers we are looking for are \(2\) and \(5\).

### Step 3: Rewrite the expression using the two numbers
We can rewrite the middle term \(7x\) using \(2x\) and \(5x\):
\[ x^2 + 2x + 5x + 10 \]

### Step 4: Factor by grouping
Now we will group the terms:
\[ (x^2 + 2x) + (5x + 10) \]

Next, we factor out the common factors from each group:
\[ x(x + 2) + 5(x + 2) \]

### Step 5: Factor out the common binomial
Now we can factor out the common binomial \((x + 2)\):
\[ (x + 2)(x + 5) \]

### Conclusion
The factored form of the expression \(x^2 + 7x + 10\) is:
\[ (x + 2)(x + 5) \]

### Final Answer
The correct option is **B. (x + 5)(x + 2)**.

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