Tu Wed Final Exam Prep/ Review Assn 2
The class webstie is a good place to see what units we covered, solutions to reviews…
We studied the following units/ mini units: Functions ch 2.3, 2.4, 2.7, Quadratics ch5, Polynomials ch7, Radicals
ch8.6-8.8, Rationals ch 8.1-8.5
Polynomials CH 7 Long Division, Synthetic Division, zeros, points on a graph, table of values, solutions to equationsclass discussion and notes here:
1] How do you deal with a remainder when doing long division? Example:
2. Now try this Multiple Choice Problem:
Remainder Theorem: If f(x) is a polynomial, then the remainder from dividing f(x) by x-a (a linear factor) is
the value f(a). (a, f(a)) is a point on the graph of the polynomial.
You can use synthetic division with a linear factor only. (x+5) works but x 2 + 2 x − 5 does not work. When the
remainder is zero f(a) = 0 so (x-a) is a factor of the polynomial. When you use synthetic division and the remainder
is something else then that remainder is the y-value in your table for that x value…
3. Practice: Use synthetic division to complete the table of values, Star the roots (zeros) of the polynomial
function. Use the points to scale the y-axis and make a complete sketch of the function.
f ( x) = x 4 − x 3 − 13 x 2 + x + 12
X
-3
-2
-1
0
1
2
3
4
F(x)
Use desmos or a graphing calculator to solve the next two problems:
Consider the system of equations
− ( x − 4) + 9
f ( x) =
2
g=
( x) 2 x − 1
Solve f ( x) = g ( x) using a graphing approach follow steps below.
a. Copy a sketch of the graph to your paper. Label important points.
b. What is the solution (s) to − ( x − 4 ) + 9= 2 x − 1 ?
2
c. Use the same graph to solve − ( x − 4 ) + 9 < 2 x − 1
2
d. Use the same graph to solve − ( x − 4 ) + 9 > 2 x − 1
2
A man will build a rectangular enclosed pigpen from three lengths of chain-link fence attached to an existing brick
wall (see diagram). He can use up to 53 feet of fence and will maximize the area of the pen.
a.
b.
c.
d.
e.
f.
g.
Write an equation for perimeter
Solve for Length
Write an equation for the pigpen area in terms of length and width
Write an equation for the pigpen area in terms of width only
Graph on graphing calculator y= Area in square feet; x= width in feet
Sketch graph to your paper: Label axes with variable, words, units.
Use your graph to determine the width of a pigpen with area of 200 sq feet. What would the length be?
Determine a second option for that area (again use the graph) what would its length be? Label pts on your
sketch.
h. Find the maximum point on the graph. Describe in words what it represents in terms of the pigpen.
i. Find the dimensions of the pen that will give the maximum area.