Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5. Write the polynomial function for the graph. f (x) = (x - 2) (x - 3) (x - 5) Simplify the right side. What is the equation?

f (x) = (x - 2) (x - 3) (x - 5)

f (x) = x³ - 10x² + 31x - 30

Step-by-step explanation:

We have to write the equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5.

That means at x = 2, x = 3 and at x = 5 the function f (x) will become zero.

Therefore, (x - 2), (x - 3) and (x - 5) are the factors of the function f (x).

Ans the cubic function is f (x) = (x - 2) (x - 3) (x - 5) ... (1) (Answer)

Now, we have to simplify the right hand side of the equation (1).

Hence, f (x) = (x - 2) (x² - 8x + 15)

⇒ f (x) = x³ - 8x² + 15x - 2x² + 16x - 30

⇒ f (x) = x³ - 10x² + 31x - 30

So, this is the requires equation. (Answer)