Question

Which statement about k(x)=-x2-2x+15 is true?

A The zeros are -3 and 5, because k(x)= -(x + 3)(x - 5).
B The zeros are -5 and 3, because k(x)= -(x + 5)(x - 3).
C The zeros are -5 and -3, because k(x)= -(x + 5)(x + 3).
D The zeros are 3 and 5, because k(x)= -(x - 3)(x - 5).​

Answer 1

The zeros are -5 and 3, because k(x)= -(x + 5)(x - 3).

Explanation:

The quantity inside parentheses is equivalent to (x + 5)(x - 3). Setting this equal to zero, we get (x + 5) = 0 and (x - 3) = 0, so the zeros are {-5, 3}.

Answer 2

The zeros are -5 and 3, because k(x)= -(x + 5)(x - 3).

Explanation:

The function k(x)=-x2-2x+15 can be re-written as k(x) = -x^2 - 2x + 15, which in turn becomes -(x^2 + 2x - 15) after the negative sign is factored out.

The quantity inside parentheses is equivalent to (x + 5)(x - 3). Setting this equal to zero, we get (x + 5) = 0 and (x - 3) = 0, so the zeros are {-5, 3}.

Thus, Answer B is correct:

The zeros are -5 and 3, because k(x)= -(x + 5)(x - 3).