Problem

Find a polynomial of degree 3 with real coefficients and zeros of −3,−1, and 4 , for which f(−2)=−30.

Answer

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Answer

Final Answer: The polynomial of degree 3 with real coefficients and zeros of -3,-1, and 4 , for which f(−2)=−30 is −5(x+3)(x+1)(x−4).

Steps

Step 1 ：The polynomial of degree 3 with zeros at -3,-1, and 4 can be written in the form f(x)=a(x+3)(x+1)(x−4) for some real number a.

Step 2 ：We can find the value of a by substituting x=−2 into the equation and setting it equal to −30.

Step 3 ：Solving for a, we find that a=−5.

Step 4 ：Substituting a=−5 back into the equation, we get the polynomial f(x)=−5(x+3)(x+1)(x−4).

Step 5 ：Final Answer: The polynomial of degree 3 with real coefficients and zeros of -3,-1, and 4 , for which f(−2)=−30 is −5(x+3)(x+1)(x−4).

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