Math 121, Quiz 4, 25 October 2004
Name:
Instructions. Complete questions 1(a), 2, 3(a) and 4. The others are for practice.
1. Determine the far right and far left behavior of the polynomials:
(a) P(x) = −x7+ 2000000x5+ 7x2
−12.
(b) Q(x) = 10x4
−50000x3+ 7.
2. Find the x-intercepts of P(x) = (x−3000)3(x−2000)2(x+ 1000)1(x+ 3000)2000. For each
intercept, determine whether the graph of P(x) crosses or merely touches the x-axis.
3. Consider the polynomial P(x) = 6x5
−3x4+ 12x2+ 13x+ 4.
(a) Use the Rational Zero Theorem to list the possible rational zeros of P(x)
(b) Use the Zero Location Theorem to prove there is a zero between x=−1 and x= 0. Do
not find that zero.
(c) Use Descartes’ Rule of signs to determine the number of positive and the number of negative
real zeros that P(x) may posses.
4. Using the information that the polynomial P(x) = 2x4
−x3
−3x2
−31x−15 has factors
(x+1
2) and (x−3), find all zeros of P(x).