Question

question 1 of 10
which statement about $y = x^2 + 5x - 24$ is true?

a. the zeros are $-3$ and $8$, because $y = (x - 3)(x + 8)$.

b. the zeros are $-3$ and $8$, because $y = (x + 3)(x - 8)$.

c. the zeros are $3$ and $-8$, because $y = (x - 3)(x + 8)$.

d. the zeros are $3$ and $-8$, because $y = (x + 3)(x - 8)$.

Explanation:

Step1: Factorizar el trinomio

Para factorizar \( y = x^2 + 5x - 24 \), buscamos dos números que sumen 5 y multipliquen -24. Estos números son 8 y -3, ya que \( 8 + (-3) = 5 \) y \( 8 \times (-3) = -24 \). Entonces, la factorización es \( y = (x + 8)(x - 3) \) o \( y = (x - 3)(x + 8) \).

Step2: Encontrar los ceros

Los ceros de la función se encuentran resolviendo \( (x - 3)(x + 8) = 0 \). Esto da \( x - 3 = 0 \) o \( x + 8 = 0 \), es decir, \( x = 3 \) o \( x = -8 \).

Answer:

C. The zeros are 3 and -8, because \( y = (x - 3)(x + 8) \).