Math 0320 Final Exam Review

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Factor out the GCF using the Distributive Property.1) 6x3 + 9x 1)

Objective: (6.1) Factor Out GCF

2) 3x2y6 + 15x2y5 2)Objective: (6.1) Factor Out GCF

Factor by grouping.3) 40r2 + 25ry - 8xr - 5xy 3)

Objective: (6.1) Factor by Grouping

4) x2 + 5x + xy + 5y 4)Objective: (6.1) Factor by Grouping

Factor, if possible, using the difference or sum of squares. If a polynomial is not factorable, write "prime."5) 100 - y2 5)

Objective: (6.2) Factor Sum or Difference of Squares

6) 49x2 + 4 6)Objective: (6.2) Factor Sum or Difference of Squares

Factor the trinomial completely using the general factoring strategy. If a trinomial is not factorable, write "prime."7) 8x3 + 18x2 + 9x 7)

Objective: (6.3) Factor Using General Strategy

8) 24x3 - 104x2 - 80x 8)Objective: (6.3) Factor Using General Strategy

Determine if the trinomial is a perfect square trinomial. If it is, factor it. If it is not, write "prime."9) z2 - 2z + 1 9)

Objective: (6.4) Factor Perfect Square Trinomial

10) 25x2 + 30x + 9 10)Objective: (6.4) Factor Perfect Square Trinomial

Factor the polynomial completely using the general factoring strategy. If the polynomial is not factorable, write "prime."11) y3 + 49y2 + 50y 11)

Objective: (6.5) Factor Out Common Factor

12) 3(x - 2) - a(x - 2) 12)Objective: (6.5) Factor Out Common Factor

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Math 0320 Final Exam ReviewSimplify the rational expression.

13) 3x - 15x2 - 25

13)

Objective: (7.1) Simplify Rational Expression

14) 5x - 215x2 + 4x - 4

14)

Objective: (7.1) Simplify Rational Expression

Multiply the rational expressions and write the answer in lowest terms.

15) 21m5p2m + p

·m - p3m8p

15)

Objective: (7.2) Multiply Rational Expressions

16) d3 + 125d - 7

·d2 - 7d

d2 - 5d + 2516)

Objective: (7.2) Multiply Rational Expressions

Divide the rational expressions and write the answer in lowest terms.

17) 2k2 + 17k + 219k2 - 24k + 16

÷ 6k2 + 17k + 12

9k2 - 1617)

Objective: (7.2) Divide Rational Expressions

18) x2 + 7x + 10x2 + 10x + 25

÷ 10 + 3x - x2

2x2 - 5018)

Objective: (7.2) Divide Rational Expressions

Simplify using the product rule for radicals.19) 490 19)

Objective: (8.1) Simplify Using Product Rule

20) 500 20)Objective: (8.1) Simplify Using Product Rule

Simplify. Assume that all variables represent real numbers.

21) -49m2

n221)

Objective: (8.1) Simplify Square Root

22) (x - 1)2 22)Objective: (8.1) Simplify Square Root

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Math 0320 Final Exam ReviewMultiply. Write the answer in simplified radical form. Assume that all variables represent positive real numbers.

23) 5y · 35y 23)Objective: (8.2) Multiply Square Roots

24) 3x3 · 6x2 24)Objective: (8.2) Multiply Square Roots

Divide. Write the answer in simplified radical form. Assume that all variables represent positive real numbers.

25) 966

25)

Objective: (8.2) Divide Square Roots

26) 3 2002

26)

Objective: (8.2) Divide Square Roots

Solve and write the solution using set notation.27) -7x - 10 = x + 4 27)

Objective: (8.3) Solve Equation Containing Square Root (Square Binomial)

28) x + 1 = x + 5 28)Objective: (8.3) Solve Equation Containing Square Root (Square Binomial)

Simplify using the product rule or quotient rule for radicals. Write the answer in simplified radical form. Assume that allvariables represent positive real numbers.

29)3

135 29)Objective: (8.5) Simplify Radical Using Product Rule or Quotient Rule

30)5

32 x4 y28 30)Objective: (8.5) Simplify Radical Using Product Rule or Quotient Rule

Evaluate.31) 272/3 31)

Objective: (8.5) Evaluate with Rational Exponents

32) 16 9

1/232)

Objective: (8.5) Evaluate with Rational Exponents

Find the functional value and write the answer as an ordered pair.33) h(x) = 3x2 - 7x - 4, h(-5) 33)

Objective: (9.1) Find Functional Value (Number)

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Math 0320 Final Exam Review34) f(t) = -3t3 + 6t2 - t - 41, f(-2) 34)

Objective: (9.1) Find Functional Value (Number)

Find the functional value.35) g(x) = 2x2 - 5x - 3, g(x - 1) 35)

Objective: (9.1) Find Functional Value (Variable Expression)

36) f(x) = 8x + 8, f(a + h) - f(a)h

36)

Objective: (9.1) Find Functional Value (Variable Expression)

Find the following function and its domain.

37) Let f(x) = 4x - 2

and g(x) = 3xx2 - 4

. Find (f + g)(x). 37)

Objective: (9.2) Find Sum, Difference, Product, or Quotient of Functions

38) Let f(x) = 2x2 - 3 and g(x) = 7x - 4. Find (f - g)(x). 38)Objective: (9.2) Find Sum, Difference, Product, or Quotient of Functions

39) Let f(x) = 5x2 - 2 and g(x) = 4x + 1. Find (f · g)(x). 39)Objective: (9.2) Find Sum, Difference, Product, or Quotient of Functions

40) Let f(x) = 5x + 1 and g(x) = 2x - 5. Find fg

(x). 40)

Objective: (9.2) Find Sum, Difference, Product, or Quotient of Functions

Perform the indicated operations and write the answer in the standard form a + bi.41) (-9 + 14i) - (5 - 2i) 41)

Objective: (10.1) Add or Subtract Complex Numbers

42) (-6 - 7i) + (12 + 4i) 42)Objective: (10.1) Add or Subtract Complex Numbers

43) (7 - 4i)(7 + 4i) 43)Objective: (10.1) Multiply or Divide Complex Numbers

44) 1 - 2i7 + i

44)

Objective: (10.1) Multiply or Divide Complex Numbers

Solve using the Zero Factor Property.45) x(6x - 1) = 0 45)

Objective: (10.2) Solve Using Zero Factor Property

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Math 0320 Final Exam Review46) 7x2 + 19x - 6 = 0 46)

Objective: (10.2) Solve Using Zero Factor Property

Solve using the Square Root Property.

47) x2 =8149

47)

Objective: (10.2) Solve Using Square Root Property

48) (3s + 9)2 = 64 48)Objective: (10.2) Solve Using Square Root Property

Solve by completing the square.49) 3x2 + 15x = - 18 49)

Objective: (10.2) Solve by Completing the Square

50) x2 + 6x = 31 50)Objective: (10.2) Solve by Completing the Square

Solve using the Quadratic Formula.51) 5x2 + 8x = 4 51)

Objective: (10.3) Solve Using Quadratic Formula

52) 17x2 - 2x = 0 52)Objective: (10.3) Solve Using Quadratic Formula

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Answer KeyTestname: MATH_0320_FINAL_SPRING_2014_II_REVIEW

1) 3x(2x2 + 3)2) 3x2y5(y + 5)3) (8r + 5y)(5r - x)4) (x + 5)(x + y)5) (10 + y)(10 - y)6) Prime7) x(2x + 3)(4x + 3)8) 8x(3x + 2)(x - 5)9) (z - 1)2

10) (5x + 3)2

11) y(y2 + 49y + 50)12) (3 - a)(x - 2)

13) 3x + 5

14) 13x + 2

15) 7pm - 7p2

m3(m + p)

16) d2 + 5d

17) k + 73k - 4

18) -219) 7 1020) 10 5

21) -7 mn

22) |x - 1|23) 5y 724) 3x2 2x25) 426) 3027) {-2}28) {4}

29) 33

5

30) 2y5 5x4 y3

31) 9

32) 43

33) (-5, 106)34) (-2, 9)35) 2x2 - 9x + 436) 8

37) 7x + 8(x - 2)(x + 2)

, D = {x x -2 and x 2}

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Answer KeyTestname: MATH_0320_FINAL_SPRING_2014_II_REVIEW

38) 2x2 - 7x + 1, D = ( , )39) 20x3 + 5x2 - 8x - 2, D = ( , )

40) 5x + 12x - 5

, D = x x 52

41) -14 + 16i42) 6 - 3i43) 65 + 0i

44) 110

-310

i

45) 0, 16

46) -3, 27

47) -97

, 97

48) -173

, - 13

49) {-3, -2}50) {-3 - 2 10, -3 + 2 10}

51) -2, 25

52) 0, 217

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