Download Math 35 Midterm 2 Study Guide Part 2 October 22, 2013

Math 35
Midterm 2 Study Guide Part 2
October 22, 2013
1. Solve each polynomial equation by factoring.
(a) x2 − 3x − 4 = 0
Answer:
(b) 2x2 − 3x − 2 = 0
Answer:
(c) 2x3 + 2x2 − 12x = 0
Answer:
2. Solve each compound inequality, if possible Graph the solution set and write it using
interval notation.
(a) x ≤ 4 and x ≤ −4
Answer:
(b) x ≥ 2 and x ≤ −4
Answer:
(c) x ≤ 6 or x ≤ 2
Answer:
(d) x ≤ −6 or x ≥ 2
Answer:
3. Simplify each expression. Write answers using positive exponents.
(a)
x12 yz
−4x−4
−1
Answer:
(b)
12x7 y 4
18x4 y 7
Answer:
(c)
18a45 b2
12a2 b13
Answer:
(d)
(e)
3x9
2x3
−1
12x67
11x43
Answer:
−1
4. Graph each linear inequality.
(a) x − y ≤ 4
(b) x ≤ 6
(c) y ≤ 2
Answer:
Math 35
Midterm 2 Study Guide Part 2
October 22, 2013
5. Perform the indicated operation.
(a) (3x + 2y)(9x2 − 6xy + 4y 2 )
Answer: 27x3 + 8y 3
(b) (6x − 5y)2
Answer: 36x2 − 60xy + 25y 2
(c) (2x − 6y)(2x + 6y)
Answer: 4x2 − 36y 2
(d) (4x − y)(16x2 + 4xy + y 2 )
Answer: 64x3 − y 3
(e) (2x − 7y)2
Answer: 4x2 − 28xy + 49y 2
6. Factor each polynomial completely using the grouping method. Hint: None of the
polynomials are prime.
(a) 2x2 + 13x + 15
Answer:
(b) 5x2 + 13x − 6
Answer:
(c) 3x2 + 22x + 7
Answer:
(d) 8x2 + 28x + 12
Answer:
(e) 4x2 + 8x − 5
Answer:
7. Perform the indicated operation.
(a)
x−2
3x2 − 6x
÷
− 2x − 8 x + 2
Answer:
x2
(b)
3x + 3y
x2 − y 2
·
y − x x2 + 2xy + y 2
Answer:
(c)
x−4
x2 − 16
÷
12x − 18
6
Answer:
(d)
−12
4x − 1
+
3x − 6
x−2
Answer:
5
4
− 2
a
b
(e)
5b + 4
b2
x2 + 5x + 6
3xy
(f)
9 − x2
6xy
Answer:
Answer:
Page 2
Math 35
Midterm 2 Study Guide Part 2
October 22, 2013
Important:
The type of problems listed on this sheet can be found in sections: 3.5, 3.6, 4.1 − 4.4, 5.1, 5.3 − 5.9,
and 6.1 − 6.5.
Formulas Need to Know:
(1) Value of a 2 × 2 Determinant
(2) Cramer’s Rule for Systems of Two Equations in Two Variables
(3) Absolute Value Equaiton
(4) Absolute Value Inequalities of the Form < or ≤
(5) Absolute Value Inequalities of the Form > or ≥
(6) Product Rule for Exponents
(7) Quotient Rule for Exponents
(8) Power Rule for Exponents
(9) Power of a Quotient Rule for Exponents
(9) Powers of a Product and a Quotient Rules
(10) Negative Exponents
(11) Difference of Two Squares
(12) Sum of Two Cubes
(13) Difference of Two Cubes
(14) Quadratic Equation
(15) Zero - Factor Property
(16) Dividing Rational Expressions
Methods Need to Know:
(1) Solving Systems of Two Equations in Two Variables by Cramer’s Rule
(2) Multiplying by FOIL Method
(3) Multiplying by Box Method
(4) Factoring by Grouping
(5) Least Common Denominator (LCD) Table
(6) Greatest Common Factor (GCF) Table
(7) Solving Quadratic Equations by Factoring Method
(8) Long Division
(9) Simplifying Complex Fractions by Multiplying by the LCD
(10) Simplifying Complex Fractions by Division
(11) Simplifying Rational Expressions by Factoring
(12) Simplifying Rational Expressions by Factoring Out the GCF
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