1.1. The Anatomy of a Polynomial of a Single Variable 3
Exercises
- State the degree, and the constant, linear and leading coefficients of
the following polynomials:
(a) 7t5 - 6t4 + 3t2 + 1
(b) 8t5 + 22 + 3
(c) 4t3
(d) (3t - 1)(2t + 1).- Give examples of
(a) a manic polynomial of degree 7
(b) a non-manic polynomial of degree 3
(c) a polynomial of degree -oo.- Decide which of the following functions are polynomials. For each
polynomial in the list, specify its degree, its constant coefficient, its
linear coefficient, its leading coefficient, and its values at t = 0 and
t = -(l/2).
For some of the functions, you may not be able to make a firm decision
at this point. As you master more of the theory of polynomials, you
should return to them.
(4 0
(b) 3t4
(c) 3+ t2
(d) 8t2 - 3t
(e) t+t-’
(f) 8t2 + t3i4 + 2t3j2 - 3tgi4 + 8 (0 < t)
(g) sinS(arc sint) (-1 < t 5 1)
(h) sinS(arc sint) (-1 5 t 5 1)
(i) cos4(arc cost) (-1 5 t 5 1)
6) St
(k) 3t3 - 2t4 + 5t2 + 6t5
(1) gt + 4’ - 2t + 6
k-4 lwt
(n) t’12 (0 2 t)
(0) t3-t
tP> tant