Write a polynomial function in standard form with zeros at 5, -4, and 1.
Please show step by step
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if \(x=5\) then \(x-5=0\) so one factor is \(x-5\)
the other two factors are found in a similar fashion
the right answer is f(x) = x^3-2x^2 -19x +20 .. I just don't know how to show the work.
If a polynomial has a zero at k, then x - k is a factor of the polynomial.
In your case, the polynomial has a zero at 5, so x - 5 is a factor.
It has a zero at -4, so x - (-4) is also a factor. This factor is simply x + 4.
Now do the same for the zero at 1 and find its factor.
Then multiply the three factors together and collect like terms and that is the polynomial.