Answer:
the factored form of the equation is (x + 4)(x - 10). This means that the values of r and s are r = -4 and s = 10.
Step-by-step explanation:
The factored form of the equation y=x^{2} - 6x - 40 is indeed of the form (x-r) (x-s). To find the values of r and s, we need to utilize the reverse process of factoring. Here's how:
Find two numbers whose product is -40 (the constant term) and whose sum is -6 (the coefficient of the x term).
List the factors of -40: 1, 2, 4, 5, 8, 10, 20, 40.
Look for a pair that adds up to -6: 4 and -10.
Rewrite the expression with the numbers from step 1 replacing the x term.
y = x^2 + (4)x + (-10)x - 40
Group the terms with common factors and factor out those terms.
y = (x^2 + 4x) + (-10x - 40)
y = x(x + 4) - 10(x + 4)
Notice the common factor (x + 4) and factor it out.
y = (x + 4)(x - 10)
Therefore, the factored form of the equation is (x + 4)(x - 10). This means that the values of r and s are r = -4 and s = 10.
