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Find a polynomial with a degree of 3, and the zeros 1,7, & -4 with no other zeros.

User Kemp
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1 Answer

4 votes

Answer:

f(x) = x³ - 4x² - 25x + 28

Explanation:

Given the zeros x = 1, x = 7 and x = - 4 , then the corresponding factors are

(x - 1), (x - 7), (x + 4)

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

f(x) = a(x - 1)(x - 7)(x + 4) , a is a multiplier

let a = 1 and expand the first pair of factors using FOIL

f(x) = (x² - 8x + 7)(x + 4) ← distribute

= x³ - 8x² + 7x + 4x² - 32x + 28 ← collect like terms

= x³ - 4x² - 25x + 28

User Styks
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