What is the correct answer?

Option (3)

Explanation:

From the graph attached,

Zeros of the function are, x = -3,

Graph of the polynomial touches x axis at x = -3, 1 and 3

Therefore, equation of the given function will be in the form of,

P(x) =

Since, graph of the function just touches the x-axis, multiplicity of zero at x = -3 will be even and crosses x-axis so the multiplicity at x = 1 and 3 will be odd.

Therefore, possible function will be,

P(x) =

Since, y-intercept of the function is at (0, -3),

P(0) = k(0 + 3)²(0 - 1)(0 - 3)

-3 = 27k

k =

Therefore, given polynomial function is,

P(x) =

Option (3) will be the correct option.

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