Two students discuss the polynomial p(x)=−3x4+5x2−7. Student A says that it is a trinomial of degree 4, while Student B claims it is a binomial of degree 4 because the subtraction sign joins two terms.
Study their arguments and answer the questions below.
(i) Which student is correct? Give a clear reason for your choice.
(ii) Explain the difference between the degree of a polynomial and the number of terms it contains.
(iii) Simplify the expression q(x)=2x5+x5−8. After simplification, state the degree of q(x) and classify it as a monomial, binomial or trinomial.