Finding a polynomial of a given degree with given zeros: Real... Find a polynomial $f(x)$ of degree 5 that has the following zeros. 7 (multiplicity 2 ), $-5,-1,0$ Leave your answer in factored form.

Step 1 ：The problem is asking for a polynomial of degree 5 with given zeros. The zeros are 7 (with multiplicity 2), -5, -1, and 0.

Step 2 ：A polynomial with given zeros can be found by multiplying factors of the form \((x - a)\), where \(a\) is a zero of the polynomial. If a zero has a multiplicity of \(n\), then the factor \((x - a)\) should be raised to the power of \(n\).

Step 3 ：In this case, the polynomial can be found by multiplying the factors \((x - 7)^2\), \((x + 5)\), \((x + 1)\), and \(x\).

Step 4 ：\(f(x) = x(x - 7)^2(x + 1)(x + 5)\)

Step 5 ：\(\boxed{f(x) = x(x - 7)^2(x + 1)(x + 5)}\)