Review #4 Exponents, FOIL, Factoring, Systems



Review #4 Exponents, FOIL, Factoring, Systems

Exponents

Adding/Subtracting: Only add/subtract coefficients of like terms. EXPONENTS DO NOT CHANGE!

Example: 3x7-2x3+5x7+x3

Add the numbers in front of [pic] : 3+5=8

Add the numbers in front of x3 : -2+1=-1

ANSWER: 8x7- x3

Multiplying: Multiply coefficients, add x exponents

• Ex: [pic]

Dividing: Divide coefficients, subtract exponents and put the exponent wherever the larger exponent was: (Big – Little)

• Ex: [pic]

1. Divide -21 and 7=-3

2. [pic]: subtract the exponents 2-1=1 so a1 goes on top

3. [pic] : subtract the exponents 6-3=3 ( So b3 goes on bottom Answer: [pic]

Zero: Anything to the zero power equals 1

• [pic] The whole quantity has the power of zero.

[pic] Note that only x is raised to the zero power, so only [pic] the rest of the factor remains.

Fractions: Fractions as exponents become radicals POWER OVER ROOT

EX: [pic]([pic]

Multiply Polynomials: If given two polynomials, use FOIL or the box method to multiply.

• Ex: [pic] box

| [pic] | [pic] | [pic] |

| [pic] | [pic] | [pic] |

Factor [pic]

1. When factoring a trinomial, factor out any GCF(number and/or variable) between all three terms.

2. Find the factors of this multiplied number that add to the middle term

Example: [pic] Numbers that Multiply to 14= 1 & 14, 2 & 7

The factors that add to 9 from above= 2& 7

Systems of Equations:

To write equations, identify x and y variable then write equation for each situation. Then choose method to solve.

3 Methods to Solve:

1. Graphing: Solve both equations for y, graph in y=, find intersection (2nd trace(5:intersect)

2. Substitution: Solve one equation for variable, plug into second equation to solve for chosen variable, plug solution into original equation for final answer

3. Elimination: Choose variable to eliminate, multiply so coefficients are equal and signs are opposite. Add straight down equations and solve for variable that is leftover. Plug solution back in for ordered pair answer.

3 Types of Solutions: one solution (x=3), no solution (5=2), and many solutions (4=4)

Systems of Inequalities:

1. Graph each inequality (solve for y first!)

2. SOLID if [pic] DOTTED if

3. Shade above for greater than, below for less than

4. Overlap region is solution

Practice:

1. Simplify: 7x2 – 5x – 3 + 2x

A. 7x2 + 3x – 3 B. x4 C. -3 D. 7x2 – 3x – 3

2. Simplify [pic]

A. -15c15d8 B. -15c8d C. -15c8d6 D. -8c8d8

3. Simplify [pic]

A. -15x2y3z3 B. [pic] C. [pic] D. [pic]

4. Simplify[pic]

A. 12b4c6 B.36b4c6 C. 12b4c5 D. 36b4c5

5. Simplify. [pic]

A. [pic] B. [pic] C. 5t6 D. 0

6. Simplify[pic]

A. [pic] B. [pic] C.[pic] D. [pic]

7. Simplify[pic]

A. [pic] B.[pic] C. [pic] D. [pic]

8. Find the perimeter of a triangle whose sides are

(3x2 + 5);(5x – 2); and (6x2 + 5x)

A. 9x2 + 10x + 3 B. 19x2 + 3

C. 9x4 + 10x2 – 3 D. 7x4 + 10x – 3

9. Simplify[pic]

A. 4x2 – 15 B. 4x2 – 4x – 15

C. 4x2 + 4x – 15 D. 8x – 15

10. Simplify (3x2 + 5x + 1) – (7x2 – 2)

A. -4x2 + 5x + 3 B. -4x2 + 5x -1

C. x2 – 1 D. x2 + 3

11. Simplify [pic]

A. 3x3 – 7x2 + 6x – 8 B. 3x3 – 6x2 + 6x + 4

C. 3x3 + 7x2 – 6x – 8 D. 2x3 – 8

12. Find the perimeter of a rectangle if the width is

(2x – 4) and the width is (5x + 1).

A. 7x – 3 B. 7x + 3 C. 14x – 6 D. 14x + 6

13. Find the area of a triangle if the base is

(2x – 4) and the height is (x + 6)

A. x2 + 4x – 12 B. 2x2 + 8x – 24

C. 2x2 – 8x – 24 D. 3x + 2

14. Simplify [pic]

|A. |2xy – 3 + 4x |B. |2y – 3 + 4x |

|C. |2y – 3 + 4xy |D. |2xy – 3 + 4x2 |

15. [pic]

A. [pic] B. [pic] C. [pic] D. [pic]

16. [pic]

A. [pic] B. [pic] C. [pic] D. [pic]

17. The area of a rectangle is given by the expression of x[pic]- 5x - 6. The length and width only have integral coefficients. Which of the following could represent the length of the rectangle?

|A. |x – 6 |B. |x – 2 |

|C. |x – 3 |D. |x – 1 |

18. Given [pic] What is x+y?

19. A restaurant received 270 hamburger patties and 350 hotdogs on Monday for $450. On Friday the restaurant received 550 hamburgers and 425 hotdogs for $630.

a. How much did each hamburger cost?

b. How much will 25 hamburgers and 50 hotdogs be?

20. A local pet store has triple the amount of fish as birds and has a total of 250 fish and birds. Write a system of equations that represents the number of fish and birds using the variables F and B.

21. Given the system of equations [pic] what is the value of x?

22. Given: 2x + y = 15

5x - 6y = -22 What is the value of x - y?

A. 11 B. 2 C. 3 D. -3

23. Given: w = 1 - v

2v + w = 4 Find the value of w.

A. 3 B. 2 C. 1 D. -2

24. A limousine company charges a flat-fee of $80 plus $.05 per mile. A shuttle van company charges a flat-fee of $60 plus $.50 per mile. Approximately what mileage will yield the same fare for both?

A. 24 miles B. 34 miles C. 44 miles D. 54 miles

25. The price of six sodas and four candy bars is $18.50. The price of two candy bars and eight sodas is $20.50. What is the price of a candy bar?

A. $1.25 B. $2.25 C. $1.65 D. $2.15

26. The area of a rectangle is given by the expression of x[pic]- 5x - 6. The length and width only have integral coefficients. Which of the following could represent the length of the rectangle?

A. x - 6 B. x - 3 C. x - 2 D. x - 1

Factor 27-30:

27. [pic] 28. [pic] 29. [pic] 30. [pic]

31. The restaurant makes at least 50 pizzas a night, but no more than 250 pizzas. The restaurant makes at least 20 salads but no more than 90 salads. A total of less than 325 pizzas and salads are made each night. Each pizza makes a profit of $3.00. Each salad makes a profit of $2.25. What is the maximum profit the restaurant can make in a night?

A. $998.25 B. $881.25 C. $907.50 D. $952.50

32. Simplify [pic] A. [pic] B. [pic] C. [pic] D. [pic]

33. Simplify [pic]

34. Solve the following system of inequalities. [pic] 35. Solve the following system of inequalities. [pic]

-----------------------

+1

2x

-3x

+5

[pic]

Rewrite the contents of the box and then combine like terms. [pic] Like terms in this example are [pic] and [pic] as well as [pic] and [pic].

ANSWER: [pic]

(x+2)(x+7)

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