Which polynomial function f(x) has a leading coefficient of 1, roots –4, 2, and 9 with multiplicity 1, and root –5 with multiplicity 3?
f(x) = 3(x + 5)(x + 4)(x – 2)(x – 9)
f(x) = 3(x – 5)(x – 4)(x + 2)(x + 9)
f(x) = (x + 5)(x + 5)(x + 5)(x + 4)(x – 2)(x – 9)
f(x) = (x – 5)(x – 5)(x – 5)(x – 4)(x + 2)(x + 9)

The expression for f(x) is:

      f(x) = (x+5)(x+5)(x+5)(x+4)(x-2)(x-9)

We know that for any polynomial equation with roots:

with multiplicity:

the equation for the polynomial is given by:

if the leading coefficient is negative we may take '-' sign in the starting of the expression.

Here we are given that :

f(x) has a leading coefficient of 1, roots –4, 2, and 9 with multiplicity 1, and root –5 with multiplicity 3

Hence, f(x) is given by:

Hence, the expression for f(x) is:

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