Before you can factor one, you have to be able to read one. Three questions do almost all the work: what is the highest power (the degree), what number rides on that highest power (the leading coefficient), and how many pieces are joined by plus and minus signs (the number of terms). Move the sliders and watch all three answers — and the graph — change together.
Your polynomial, drawn
the whole polynomialthe leading term alone
Why the leading term gets its own name
Is it even a polynomial?
0move a slider to begin
coefficient of x40
coefficient of x32
coefficient of x2−3
coefficient of x−3
constant term2
Set a coefficient to 0 and that term disappears entirely — watch the term count and, if it was the top one, the degree drop with it.