Find a polynomial function with the zeros -2, 3, 5 whose graph passes through the point (6,48)

Using the factor theorem, it is found that the polynomial function is given by:

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Factor theorem:

Given a polynomial f(x), this polynomial has roots such that it can be written as: , in which a is the leading coefficient.

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The polynomial is given by:

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Thus, the polynomial is given by:

A similar question is given at link

f(x) = 2x³ - 12x² - 2x + 60

Step-by-step explanation:

Given that the zeros are x = - 2, x = 3, x = 5 , then the factors are

(x + 2), (x - 3), (x - 5)

The polynomial is then the product of the factors, that is

f(x) = a(x + 2)(x - 3)(x - 5) ← a is a multiplier

To find a substitute (6, 48) into the polynomial

48 = a(8)(3)(1) = 24a ( divide both sides by 24 )

a = 2 , thus

f(x) = 2(x + 2)(x - 3)(x - 5) ← expand the last 2 factors using FOIL

     = 2(x + 2)(x² - 8x + 15) ← distribute the parenthesis

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

     = 2(x³ - 6x² - x + 30) ← distribute by 2

     = 2x³ - 12x² - 2x + 60

step-by-step explanation: yes