x^3 + 7x^2 − 36

The polynomial above has zeros at -6 and 2. If the remaining zero is z, then what is the value of -z?

What you have to remember here is that the zeros in a polynomial correspond to the factors of the polynomial. In other words, by telling us there are zeros at -6, 2, and z, the question is telling us that x+6, x-2, and x-z are factors of the polynomial. Which is to say:


If you’ve expanded enough polynomials, you know that without doing all the math you can conclude that -36=(6)(-2)(-z). So we can do a little math and solve for z:


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