example of a polynomial in the variable t

Question

Give an example of a polynomial in the variable t, such it is fifth degree, in descending powers of the variable, with exactly six terms, and having a negative coefficient for its second degree term.

Answer 1

t⁵ + t⁴ + t³ - t² + t + C

 

where:

C is an arbitrary constant term. 

-t² is a term with degree of 2, since the exponent of t is 2 and with a coefficient of -1.

The first term has an exponent of 5 since the overall polynomial is of degree 5.

 

 

Some key degrees you want to know:

1st degree indicates straight line polynomial.

2nd degree indicates parabolic polynomial.

3rd degree indicates cubic polynomial (looks like an S-shape curve).