Polynomial equations sometimes come in disguise. For example, the formula:
y = (x +1) · (x  4)^{2} = (x +1) · (x  4) · (x  4)
does not look like a polynomial equation because it does not closely resemble the
standard form of a polynomial equation given above.
However, if you FOIL this formula and carefully simplify then you can get the equation
to resemble the standard form, and confirm that it is, indeed, a polynomial
equation.
Doing this:
y = (x +1) · (x  4) · (x  4) 
(FOIL (x  1) and (x  4))

y = (x^{2}  3 · x  4) · (x  4) 
(FOIL again) 
y = x · (x^{2}  3 · x  4)  4 · (x^{2}  3
· x  4) 
(Multiply through) 
y = x^{3}  3 · x^{2}  4 · x  4 · x^{2} +12
· x +16 
(Collect like terms) 
y = x^{3}  7 · x^{2} + 8 · x +16 
(Collect like terms) 
This looks exactly like the standard form of the formula for a polynomial
equation. So,
although the equation did not initially look very much like a polynomial
equation, it
turned out to be a polynomial because it was possible to expand and simplify the
equation, eventually making it resemble the standard form for a polynomial
equation.
