**1. Simplify the expression 3a(2b-a)-2b(2+4a)+5a+b(a+b-6) and fill in the blanks below.**

___________ a^{2}+ ___________b^{2}+___________ab+___________a+__________b

**2. The polynomial, x^3+7x^2-20x-96, has a factor of (x+8). Which of the following represents two of the zeros of the polynomial?**

- x=-3 and x=4
- x=-6 and x=2
- x=-3 and x=-4
- x=6 and x=-2

**3. The possible combinations of candy bars and packages of suckers that Amanda may purchase are represented by the graph shown below.**

**Which of the following inequalities represents the possible combinations of candy bars and packages of suckers that she may purchase?**

- 0.75x+1.5y=20
- 0.5x+1.25y=25
- 0.75x+1.25y=25
- 1.25x+0.75y=20

**4. Part A: Sketch the function y=3x^2+6x-2 on the graph below.**

**Part B: On what intervals of x is the function increasing?**

________________________________________

**5. Ana solves the quadratic equation, x^2-6x=18, by completing the square. Which of the following equations may be used to find the solution, using this method?**

- ?(x+3)?^2=27
- ?(x-6)?^2=24
- ?(x+6)?^2=24
- ?(x-3)?^2=27

## Answers

1. Use order of operations to solve. 3a(2b-a)-2b(2+4a)+5a+b(a+b-6)=6ab-3a^2-4b^2-8ab+5a+ab+b^2-6b=3a^2-3b^2-1ab+5a-6b. So filling in the blanks:

2. A: Since the polynomial has a factor of x+8, synthetic division of the given polynomial by -8 may be completed. Recall the factor is in the form, (x-a); equals , so a=-8. Synthetic division reveals x^3+7x^2-20x-96=(x+8)(x^2-x-12).The factor x^2-x-12, which can be further factored as (x+3)(x-4). Setting each factor equal to zero gives x=-3 and x=4. Thus, two more zeros of the polynomial are x=-3 and x=4. The zero that may be directly determined from the problem is x=-8.

3. C: The y-intercept of the inequality is 20, and the slope is -0.6. The slope can be determined by calculating the ratio of the change in y-values per change in corresponding x-values. Using the y-intercept and the point, (25, 5), the slope can be written as (5-20)/(25-0), which equals -0.6. Since the evaluation of the inequality for x- and y-values at the origin produces a true statement, the side of the plane containing the point, (0, 0) should be shaded. The inequality, 0.75x+1.25y=25, solved for y, may be written as y=-0.6x+20. Thus, Choice C is the correct answer.

4. Part A: The graph should look like:

Part B: The function increases from x=-1 to x=8

5. D: When completing the square, the coefficient of the x-term, or -6, should be divided by 2 and then squared. Doing so gives 9. This constant should be added to both sides of the equation. Thus, the equation may be written as x^2-6x+9=27. The left side of the equation may be written as ?(x-3)?^2. Thus, the equation that may be used to find the solution of the equation, using the method of completing the square, is ?(x-3)?^2=27.

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by Enoch Morrison | Last Updated: January 9, 2019