Question

If x^2 - 2x - 15 = (x + r)(x + 8) for all values of x, what is one possible value of r?

a) r = 5
b) r = 3
c) r = -3
d) r = -5

Answer 1

The value of r in the factored expression (x + r)(x + 8) for the equation x^2 - 2x - 15 is -5, as it satisfies the requirements for the coefficients and constant in the quadratic equation.

Step-by-step explanation:

To determine the value of r, let's factor the quadratic equation x^2 - 2x - 15. The equation can be expressed in the form of (x + r)(x + 8), as given in the question. To find r, we need to factor the quadratic equation in such a way that the product of the two numbers is -15 (the constant term) and their sum is -2 (the coefficient of the x term).

The factors of -15 that add up to -2 are -5 and 3. Since we need a sum of -2, we combine -5 with positive 3, so the factors will be (x - 5)(x + 3). Comparing this to the provided format (x + r)(x + 8), we can see that r should be equal to -5 to maintain the equivalence of the two expressions. Therefore, the correct value of r is -5.