We appreciate your visit to Using the Factor Theorem which of the polynomial functions has the zeros 4 7 and 4 A f x x 3 4x 2 7x 28. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
The polynomial functions Of(x) = x³+4x²-7x-28, Of(x) = x³-4x²-7x+28, and Of(x) = x³-4x²-7x+28 have the zeros 4, 7, and -, respectively.
Explanation:
The Factor Theorem states that a polynomial function has a factor (x - c) if and only if the remainder is zero when the function is divided by (x - c). To find which of the given polynomial functions have zeros at 4, 7, and -, we substitute these values into each function and check if the result is zero.
Substituting 4 into the given polynomial functions, only Of(x)= x³+4x²-7x-28 results in zero. Therefore, this function has the zeros 4.
Similarly, substituting 7 into the given polynomial functions, only Of(x)= x³-4x²-7x+28 results in zero. Hence, this function has the zeros 7.
Finally, substituting - into the given polynomial functions, only Of(x)= x³-4x²-7x+28 results in zero. Thus, this function has the zero -.
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