Saturday, November 5, 2011

Sample Test Questions - Factoring and Solving

Sample 10-question Elementary Algebra test covering topics found in Chapter 6 - Factoring and Solving by Factoring.

1. Factor.


Four term polynomial - factor by grouping.



2. Factor.


Three-term polynomial - factor trinomials using the trial and error technique.


3. Factor.


Two-term polynomial - first factor out the GCF. Then factor the resulting special binomial factors completely.


4. Solve.


First multiply to obtain standard form, equal to zero. Then factor and set each factor equal to zero.


5. Solve.


Factor and then set each variable factor equal to zero.


6. Find a quadratic equation with integer coefficients that has the following solutions:


Work the process for solving by factoring in reverse.


7. Given

a. Calculate f(0).
b. Find all values of x for which f(x) = 0.


8. The product of two consecutive positive odd integers is eleven less than 10 times the larger. Find the integers.


9. The length of a rectangle is 6 cm longer than twice its width. If the area is 140 cm^2, find the dimensions of the rectangle.


10. The cost of a particular car in dollars can be approximated by the function
 
where x represents the age of the car in years (graphed below).



a. Use the graph to determine the cost of the car when it was new?
b. Use the graph to determine how old the car will be when it reaches its minimum cost?
c. Use the function to determine how much this car will be worth when it reaches 5 years old?