Question

select the correct answer.

which point is a point where the graph of (y = (x - 5)(x^2 - 7x + 12)) crosses the (x)-axis?

(a) ((-5,0))
(b) ((-3,0))
(c) ((4,0))
(d) ((12,0))

Explanation:

Set \(y = 0\) to find the x-intercepts

$$ (x - 5)(x^2 - 7x + 12) = 0 $$

Factor the quadratic expression

$$ x^2 - 7x + 12 = (x - 3)(x - 4) $$

Solve for the zeros of the function

$$
LATEXBLOCK0
$$

The corresponding points on the x-axis are \((5,0)\), \((3,0)\), and \((4,0)\).

Answer:

• (-5,0)
• (-3,0)
• (4,0) (Correct answer)
• (12,0)