2) List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which actually are zeros). (Enter your answers as a comma-separated list.)

R(x) = 2x⁵ + 9x³ + 9x² 6

x =

3) A polynomial P is given.

P(x) = x⁴ + 18x² + 81

(a) Find all zeros of P, real and complex. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)

x =

(b) Factor P completely.

P(x) =

4) A function is given.

f(x) = x³ 9x²; x = 0, x = 10

(a) Determine the net change between the given values of the variable.

(b) Determine the average rate of change between the given values of the variable.

6)Use synthetic division and the Remainder Theorem to evaluate P(c).

P(x) = 3x² + 12x + 5, c = 1

P(1)=

8) Use

f(x) = 2x 3 and g(x) = 5 x² to evaluate the expression.

(a) f(f(2)) =

(b)

g(g(3)) =

9) Factor the polynomial completely.

Q(x) = x⁴ + 18x² + 81

Q(x) =

Find all its zeros. State the multiplicity of each zero. (Order your answers from smallest to largest real, followed by complex answers ordered smallest to largest real part, then smallest to largest imaginary part.)

x	=		with multiplicity
x	=		with multiplicity

11) Sketch the graph of the function by first making a table of values.

f(x) = x + 3, 3 x 3

x	f(x) = x + 3
3
2
0
1
2
3

14) Find all the real zeros of the polynomial. Use the quadratic formula if necessary, as in Example 3(a). (Enter your answers as a comma-separated list. Enter all answers including repetitions.)P(x) = x⁴ 9x³ + 10x² + 27x + 7

x =

16) Find the quotient and remainder using synthetic division.

x^5+4x^3-14over x-

quotient
remainder

20) A function f is given.

f(x) = 4 2x, 1 < x < 5

(a) Sketch a graph of f.

(b) (b) Use the graph to find the domain and range of f. (Enter your answers using interval notation.)

Domain

Range

21) Factor the polynomial and use the factored form to find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)

P(x) = x³ + 3x² 9x 27

x = Sketch the graph.

24) Factor the polynomial completely.

P(x) = x⁵ + 2x³

P(x) =

Find all its zeros. State the multiplicity of each zero. (Order your answers from smallest to largest real, followed by complex answers ordered smallest to largest real part, then smallest to largest imaginary part.)

x	=		with multiplicity
x	=		with multiplicity
x	=		with multiplicity

27)A quadratic functionfis given.

f(x) =x²4x+7

(a) Expressfin standard form.

f(x)

=

(b) Find the

vertex

x intercepts

y-intercepts off. (If an answer does not exist, enter DNE.

(c) Sketch a graph off.

(d) Find the domain and range of f. (Enter your answers using interval notation.)

29) All the real zeros of the given polynomial are integers. Find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)

P(x) = x³ + 7x² x 7

x = Write the polynomial in factored form.

P(x) =

30) Use f(x) = 5x 4 and g(x) = 2 x² to evaluate the expression.

(a) (f g)(2)

(b) (g f)(2)

31) Sketch the graph of the function, not by plotting points, but by starting with the graph of a standard function and applying transformations.

f(x) = x³