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:

Step1: Set $y=0$ for x-intercepts

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

Step2: Factor quadratic term

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

Step3: Solve for $x$ values

$x-5=0 \implies x=5$; $x-3=0 \implies x=3$; $x-4=0 \implies x=4$

Step4: Match to options

The valid x-intercepts are $(5,0)$, $(3,0)$, $(4,0)$.

Answer:

C. (4,0)