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4 years ago

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

Mathematics

1 answer:

nasty-shy [4]4 years ago

4 0

Answer:

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

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