Practice Test

1) A 12” by 18” piece of sheet metal has equal-sized squares cut from each corner so it may
be folded and formed into a topless box. What dimensions of the finished box will
maximize the volume of the box?
2) Let f(x) be the function graphed below. List the transformations. Then, graph
⎛1⎞ gx ( ) =−2 f⎜ ( x−
2) ⎟+
1
⎝3⎠

3) Find the roots and factor over the rationals and reals:
f x x x x x
4 3 2
( ) = 2 + + 11 + 26 − 16
4) Find the roots and factor over the rationals and completely. Then give the multiplicity of
4 3 2
each root: gx ( ) = 3x− 17x+ 47x− 75x+ 50

5) Graph
6) Solve:
x(2x+ 1)( x− 4)( x+
2)
f( x)
=
( x− 3)( x+ 2)( x+
5)
x
2
−1
2
2x − 5x+ 3
> 1
2x − 3x+ 1
7) Determine the equations of any horizontal and vertical asymptotes of f( x)=
2
x −1
2

3
2
8) Evaluate g( x)=− 3x+ 6x−1
for x = -2 using synthetic division.
9) Use long division to divide. Write your answer in the form f ( x) = h( x) ⋅ q( x) + r .
3 2
2
( x − 7x + 12x− 30)
÷ ( x − 2)
2
10) Solve the inequality 3x− 11x> 20 and write your answer in interval notation.

11) Find the equation of a polynomial with integer coefficients that has zeros of
2
, 41 , − 3i.
3
12) Write the quotient in standard form:
6+ 5i
1−3i .