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Answer :
Final Answer:
By Using the Factor Theorem, f (x) = x³ – 4x² – 7x + 28 polynomial functions has the zeros 4, √7 , and -√7.
The correct option is b. f (x) = x³ – 4x² – 7x + 28.
Explanation:
The Factor Theorem states that if a polynomial function has a zero, then the corresponding factor is also present in the polynomial. In this case, the zeros are 4, √7, and -√7.
Let's break down the options and see which one matches the given zeros:
a. f (x) = x³ – 4x² + 7x + 28
b. f (x) = x³ – 4x² – 7x + 28
c. f (x) = x³ + 4x² – 7x + 28
d. f (x) = x³ + 4x² – 7x – 28
For a zero of 4, the factor is (x - 4).
For zeros of √7 and -√7, the factors are (x - √7) and (x + √7), respectively.
Now, let's multiply these factors:
(x - 4)(x - √7)(x + √7)
(x - 4)(x² - 7)
Expanding, we get:
x³ - 4x² - 7x + 28
This matches the polynomial function in option b. Thus, the polynomial function **f (x) = x³ – 4x² – 7x + 28** has the given zeros.
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