Answer:
(r - 6)(r - 10).
Explanation:
To factor the quadratic expression r² - 16r + 60, we can use the factoring method.
Step 1: Look for two numbers that multiply to give you the constant term (60) and add up to give you the coefficient of the middle term (-16).
In this case, we need to find two numbers that multiply to 60 and add up to -16.
The numbers that satisfy these conditions are -6 and -10, since (-6) * (-10) = 60 and (-6) + (-10) = -16.
Step 2: Rewrite the middle term (-16r) using the two numbers found in Step 1.
r² - 6r - 10r + 60
Step 3: Group the terms and factor by grouping.
(r² - 6r) - (10r - 60)
Step 4: Factor out the greatest common factor from each group.
r(r - 6) - 10(r - 6)
Step 5: Notice that we now have a common factor of (r - 6) in both terms.
(r - 6)(r - 10)
Therefore, the factored form of r² - 16r + 60 is (r - 6)(r - 10).