ACC AAF W/S #2 - Key

1. ACCUPLACER® Module #3 - AAF Worksheet #2 Key 1

2. Module #3 Worksheet #2 1. A: Finding the product means distributing one polynomial to the other so that each term in the first is multiplied by each term in the second. The like terms can be collected. Multiplying the factors yields: Collecting like terms means adding the x2 terms and adding the x terms. The final answer after simplifying the expression is: 2. D: Finding the zeros for a function by factoring is done by setting the equation equal to zero, then completely factoring. Since there was a common x for each term in the provided equation, that is factored out first. Then the quadratic that is left can be factored into two binomials: (x + 1) (x -4).Setting each factor equation equal to zero and solving for x yields three zeros. 3. D: Dividing rational expressions follows the same rule as dividing fractions. The division is changed to multiplication, and the reciprocal is found in the NAME: ______KEY________________      3 2 2 20 4 24 40 8 48. x x x x x    3 2 20 36 16 48. x x x 3 9 5 3 3 x x y second fraction. This turns the expression into: . Multiplying across and * 2 25 8 xy simplifying, the final expression is: . 5 4. B: The equation can be solved by factoring the numerator into (x + 6) (x - 5). Since that same factor (x - 5) exists on top and bottom, that factor cancels. This leaves the equation x + 6 = 11. Solving the equation gives the answer x = 5. When this value is plugged into the equation, it yields a zero in the denominator of the fraction. Since, this is undefined, there is no solution. 5. C: Graphing the function y = cos(x) shows that the curve starts at (0, 1), has an amplitude of 2, and a period of 2?. This same curve can be constructed using the  units. This equation is in the form sine graph, by shifting the graph to the left 2    . sin( ) y x 2 2