Write a polynomial function in standard form with zeros at 5, -4, and 1.
Please show step by step

Question

Write a polynomial function in standard form with zeros at 5, -4, and 1. 
Please show step by step

anonymous · Answer

if $x=5$ then $x-5=0$ so one factor is $x-5$
the other two factors are found in a similar fashion

sphott51 · Answer

the right answer is f(x) = x^3-2x^2 -19x +20 .. I just don't know how to show the work.

mathstudent55 · Answer

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.