Download Name Math 1302 – Test IV Test Review

Name ________________________________ Math 1302 – Test IV Test Review ( HW )
1. This is the same question asked in several ways.
Is x = 2 a solution of the equation x4 – 2x = 4 ? _________ ( Show Work )
Is x – 2 a factor of the polynomial x4 – 2x – 4 ? __________ (show work )
What is the remainder of ( x4 – 2x – 4 ) ÷ ( x – 2 ) ? __________
Factor the polynomial x4 – 2x – 4 if x = 2 is a solution of the equation x4 – 2x – 4 = 0. ________________________
Find ( x4 – 2x – 4 ) ÷ ( x – 2 ) = ______________________
2.
If x = 2 and x = - 3 are roots of a quadratic equation, then find the quadratic equation. __________________
3.
If x = - 4 , x = 5, and x = 1 + 2i, x = 1 – 2i are all of the zeros of a polynomial ( solutions of a polynomial equation),
then what is the degree of the polynomial .
4. Given that 3 + 2i and - 5 are the roots of a polynomial, then find the least degree (n ) the polynomial must have ?
n≥ ?
n = _______
5. How roots does x5 + 2x + 1 = 0 have ? _________ How many are positive ? _______ How many are negative ? ____
What must the remaining roots be ( if they are not negative or positive) ? _________
6.
How many negative roots does x4 - 2x3 + 2x2 -5x + 3 = 0 have ? ________
What does that say about the number of positive roots ? ____________________________________________
7. Use synthetic division to find all of the roots of x3 - 2x - 4 = 0 , Hint: try 2 or – 2 .
8. Give examples of rational numbers ; ________________________________
Give me examples of irrational numbers; ________________________________
9.
Find all rational roots of x8 + 2x5 - 4x2 + 4x - 1 = 0 → ______________
10. If x = - 4 and x= 2 +
5 is a solution of an equation, find other value(s) of x that must also be solutions.
1
11.
Given P(x) = 3x5 - 2x2 + 4 find all possible rational numbers that should be tested to find the rational roots of
P(x) = 0
12. Is x + y factor of x3 + 2xy2 – y3 ?
13.
Find all of the roots of x3 - 2x + 1 = 0 if x = 1 is known to be a solution. ________________
After you find the solutions – factor the original polynomial. x3 - 2x + 1 = ___________________________
14. Find all of the zeros of the polynomial x3 - 2x2 + x – 2 = 0
15.
Find all of the zeros of x4 - 2x3 + 5x2 - 8x + 4 = 0
16. Find
( a + b)0 = _____________
ex. ( x – y )2 = ______________________________
ex. ( 2x + y)1 = ____________
ex ( x + 2y )3 = _______________________________
2
17.
What is the coefficient of the
a) first term of ( 2x + y)4 ? _____________
b) the second term of the expansion of ( x – 3y )5. _______________
c) the coefficient of the last tem of the expansion of ( 1/x + 2x ) 4. ______________
18. Sketch the graph of the following inequalities( in two variables – need to use a rectangular coordinate system).
a) 2x + y ≥ 4
c)
x - 2y ≤ 0
b)
y < x2 + 4
d) x > 3
19. Find the solution of the following system of inequalities.
a)
2x + y ≥ 2
x+y ≤4
b) x > 3
y ≤ x2
3
20. Find the solution of each of the following systems of equations by the chosen method.
a) substitution
2x + y = 4
3x – 5y = 1
b) elimination
x + 4y = 2
2x – y = 3
c) any method.
2x – 3y = 3
4x - 6y = 1
d) any method
3x + 12y = - 9
2x + 8y = - 6
21. Find the solution of each of the following system of equations.
x + 2y – 3z = 5
2x + 4y – z = 5
3x + y – 2z = 8
4
22. Solve.
x + 2y - z = - 4
2x – y
x +
23.
=3
+z =4
Direct Variation.
We say that y varies directly as x2 (direct variation – varies directly )
and write → _____________
If y = 12, when x = 3, then find y when x = 10.
We say that y varies inversely as
_________
x ( inverse variation - varies inversely)
and write → __________
If y = 2, when x = 9, then find y , when x = 16. ___________
24. Identify as direct or inverse variation.
a) the more friends you have, the happier you get. ________________
b) the more friends your best friend gets, the more jealous you get. __________
c) the more you stay up watching TV, the lower your grade gets. _____________________
d) the more you exercise, the less visits you make to the doctor. ____________
e) the higher your test grade, the higher your letter grade in class. _______________
25.
What is the dimension of the following matrices?
A =
D=
1
 2 5,
1
0

0

0
B=
 1 3 
 2 1 / 2


C=
2
4
 
0 0 0
1 0 0
0 1 0

0 0 1
5
Name _______________________________ HW – Quiz – April 24, 2006
1. Solve
2x – y ≥ 4
x≤2
2.
What quadrant is being shaded ?
x≤0
y≥0
4. Solve.
2x + y = 3
6x + 3y = 2
5.
x – 2y = 4
2x + 3y = 2
6. x2 - y 2 = 5
x2 + y2 = 3
7.
x2 + 2x + y = 3
2x – y = 4
8.
x2 + 2y2 = 9
x+y=1
6