Question

which statement about $y=x^2 - 3x - 40$ is true?
a. the zeros are 5 and $-8$, because $y=(x - 5)(x + 8)$.
b. the zeros are $-5$ and 8, because $y=(x + 5)(x - 8)$.
c. the zeros are 5 and $-8$, because $y=(x + 5)(x - 8)$.
d. the zeros are $-5$ and 8, because $y=(x - 5)(x + 8)$.

Explanation:

Step1: Factor the quadratic expression

We need two numbers that multiply to $-40$ and add to $-3$. These numbers are $-8$ and $5$. So:
$$y = x^2 - 3x - 40 = (x + 5)(x - 8)$$

Step2: Find the zeros

Set $y=0$, then solve for $x$:
$(x + 5)(x - 8) = 0$
Set each factor equal to 0:
$x + 5 = 0 \implies x = -5$
$x - 8 = 0 \implies x = 8$

Answer:

B. The zeros are -5 and 8, because $y=(x + 5)(x - 8)$.