To factor the quadratic expression x^2 + 7x + 10, we will need to find two numbers that multiply to give 10 and add up to 7.
The two numbers are 2 and 5 because 2 * 5 = 10 and 2 + 5 = 7.
Using these numbers, we can rewrite the expression as:
x^2 + 2x + 5x + 10
Now, we can group the terms:
(x^2 + 2x) + (5x + 10)
Next, we factor out the greatest common factor of each pair of terms:
x(x + 2) + 5(x + 2)
Finally, we notice that (x + 2) is a common factor of both terms, so we can factor it out:
(x + 2)(x + 5)
Therefore, the factored form of x^2 + 7x + 10 is (x + 2)(x + 5).