Answer:
To factorize the quadratic expression x² + 13x + 40, we need to find two numbers that multiply to give the coefficient of the constant term (40) and add up to give the coefficient of the linear term (13).
Let's look for two numbers that meet these criteria:
The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40.
Now, we need to find a pair of numbers from these factors that add up to 13. The pair that satisfies this is 8 and 5, because 8 + 5 = 13.
So, we can rewrite the middle term (13x) using these two numbers:
x² + 8x + 5x + 40
Now, we can group the terms and factor by grouping:
x(x + 8) + 5(x + 8)
Notice that we have a common factor of (x + 8) in both terms. We can factor it out:
(x + 8)(x + 5)
Therefore, the factored form of the quadratic expression x² + 13x + 40 is (x + 8)(x + 5).