Question

which function has zeros at x = -2 and x = 5?
○ f(x) = x² + 2x - 10
○ f(x) = x² - 2x - 10
○ f(x) = x² + 3x - 10
○ f(x) = x² - 3x - 10

Explanation:

Step1: Use zero form to write factors

If $x=-2$ and $x=5$ are zeros, then the factors are $(x+2)$ and $(x-5)$.

Step2: Multiply the two factors

$$f(x)=(x+2)(x-5)$$

Step3: Expand the product

$$f(x)=x^2 -5x +2x -10 = x^2 -3x -10$$

Answer:

$\boldsymbol{f(x) = x^2 - 3x - 10}$ (the fourth option)