Exam (elaborations) MATH 1512 (4)

1. Solve the linear equation 1 5 ሺ10ݔ െ 20ሻ ൌݔെ3 1._____ a) ሼെ1ሽ b) ሼ17ሽ c) ሼ3ሽ d) ሼ1ሽ 2. Decide whether the equation is an identity, a conditional equation, or a contradiction. 2ሺ3ݔ െ 4ሻ ൌ 6ݔ ൅ 5 2._____ a) identity b) conditional equation c) contradiction d) none of these 3. The formula for the perimeter of a rectangle is given by ܲ ൌ 2݈ ൅ 2ݓ , where ݈ is the length and ݓ is the width. Assume the perimeter of a rectangular plot of land is 480 ft. The length is twice the width. Find the length of the rectangular plot of land. 3._____ a) 80 ft b) 120 ft c) 160 ft d) 240 ft 4. A car dealership uses the linear model ݕ ൌ െ1100ݔ ൅ 25000 to predict the depreciation of car values as time progresses. If ݔ is how old the vehicle is in years and ݕ is the current value of the vehicle, what will the value of the vehicle be 5 years after purchase? 4._____ a) $18,400 b) $19,500 c) $22,700 d) $23,900 5. Find the following sum. 7ሺ3ݔଶ ൅ 2ݔ െ 5ሻ ൅ 2ሺെݔଶ ൅ 3ሻ 5._____ a) 20ݔଶ ൅ 14ݔ െ 32 b) 19ݔଶ ൅ 2ݔ െ 2 c) 28ݔଶ ൅ 14ݔ െ 28 d) 19ݔଶ ൅ 14ݔ െ 29 6. Find the following product. ሺ1 െ 3ݔሻሺݔଶ ൅ 2ݔ െ 5ሻ 6._____ a) െ3ݔଷ െ 5ݔଶ ൅ 17ݔ െ 5 b) ݔଶ െݔെ4 c) െ3ݔଷ ൅ 7ݔଶ ൅ 13ݔ െ 5 d) െ7ݔଶ ൅ 17ݔ െ 5 7. Factor out the greatest common factor from the following polynomial. 3ܽ଻ܾଷ െ 21ܽସܾଷ 7._____ a) ܽସܾଷሺ3ܽଷ െ 21ሻ b) 3ܽସܾଷሺܽଷ െ 7ሻ c) ܽସܾଷሺ3ܽଷܾ െ 21ܾܽሻ d) 3ܽସܾଷሺܽଷܾ െ 7ܾܽሻ 8. Factor the following polynomial by grouping. 15ܾܽ െ 6ܾ ൅ 10ܽ െ 4 8._____ a) ሺ3ܾ ൅ 2ሻሺ5ܽ െ 2ሻ b) ሺ3ܾ െ 2ሻሺ5ܽ ൅ 2ሻ c) ሺ3ܾ ൅ 2ሻሺ5ܽ ൅ 2ሻ d) ሺ3ܾ െ 2ሻሺ5ܽ െ 2ሻ 9. Factor the following trinomial. 6ݔଶ ൅ 11ݔ െ 10 9._____ a) ሺ3ݔ െ 2ሻሺ2ݔ െ 5ሻ b) ሺ3ݔ ൅ 2ሻሺ2ݔ െ 5ሻ c) ሺ3ݔ െ 2ሻሺ2ݔ ൅ 5ሻ d) ሺݔ ൅ 6ሻሺ11ݔ െ 10ሻ