Find a polynomial of the specified degree that has the given zeros.
Degree 3 ; zeros -5,5,7
P(x)=
Answer
Final Answer: The polynomial of degree 3 that has the given zeros -5, 5, and 7 is \(\boxed{P(x) = x^3 - 7x^2 - 25x + 175}\).
Step 1 ：We are given that the polynomial is of degree 3 and has zeros -5, 5, and 7.
Step 2 ：A polynomial of degree 3 with zeros -5, 5, and 7 can be written in the form of \(P(x) = a*(x - r1)*(x - r2)*(x - r3)\), where \(r1 = -5\), \(r2 = 5\), and \(r3 = 7\).
Step 3 ：The constant a can be any non-zero number, but for simplicity, we can choose \(a = 1\).
Step 4 ：Substituting the values of a, r1, r2, and r3 into the equation, we get \(P(x) = x^3 - 7x^2 - 25x + 175\).
Step 5 ：Final Answer: The polynomial of degree 3 that has the given zeros -5, 5, and 7 is \(\boxed{P(x) = x^3 - 7x^2 - 25x + 175}\).
