Download Algebra II BC

Alg 2 BC U6
Quiz Review (Day 6)
Give the end behavior of each polynomial function:
1.
y  (3  x)( x  5)2 ( x  1)3
3. Divide WITHOUT a calculator:
2.
y  25 x 4  3x 23
(4 x5  3x3  7 x  4)  (2 x  3)
4. WITHOUT a calculator, graph each polynomial.
Use x-intercepts (including the concept of MULTIPLICITY, y-intercepts and end behavior.)
(For irrational zeros, approximate the radical by determining the two integers that it lies between.)
a)
y  (3  x)( x  5)2
b)
y   x 4  2 x3  x  2
c)
y  x3  8 x 2  16 x  5
d)
y  x 4  5x 2  36
5. If
(Hint: -5 is one of the zeros.)
f ( x)  5x5  ax 2  7 x  2 , for what value of "a" does f(3)=27?
(Use synthetic substitution to solve.)
6. Classify the polynomials in 4c and 4d by DEGREE and NUMBER OF TERMS.
7. Factor:
a)
125 x12  1
b)
4 x4  109 x2  225
8. Solve each polynomial equation. The number of solutions should equal the degree of your highest term.
a)
64 y3  125
c)
2 x3  10 x  7 x 2  35
b)
x 4  2 x 2  5
d)
(Yes, these are complicated answers.)
12 x3  61x2  x  30
(One solution is 3/4.)
9. Write a polynomial equation IN STANDARD form with zeros -3 (multiplicity 2) and 4 (multiplicity 1.)
10. CALCULATOR OK: A box has dimensions 8 inches x 12 inches x 25 inches. The same number of inches is ADDED to
the two shorter dimensions and SUBTRACTED from the largest dimension. If "x" represents the number in inches
added/subtracted, write a polynomial expressing the volume of the new box. Then, use the "Calc maximum" on your
calculator to find the number of inches that should be added/subtracted in order to maximize the volume of the new box, as
well as the maximum volume (all to the nearest thousandth.) HINT: Start with a window of -20/20/1 -100/100/1. Then use
your understanding of polynomials to get to the window that you need to answer the question.