Math 40
Exam #6 Study Guide
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Date:
1. Factor the greatest common factor.
(a) 6x2 − 24x
(b) 18x2 y − 9xy − 36xy 2
2. Factor each of the following by grouping.
(a) x2 + 2ax − 3bx − 6ab
(b) xy + 4x − 7y − 28
3. Factor the following completely.
(a) y 2 − 5y + 6
(b) x2 − 16
(c) a4 − 81
(d) 27x2 − 75y 2
(e) a3 + 5a2 − 9a − 45
(f) 4x2 + 22x + 10
(g) 3m2 − 3m − 18
(h) 6x2 + 7x − 5
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(i) 12x3 − 14x2 − 10x
(j) a3 + 64b3
4. Solve the following equations.
(a) y 2 + 7y + 12 = 0
(b) x2 − 16 = 0
(c) a2 − 11a = −30
(d)
2x2 = a + 15
(e) 30x3 − 20x2 = 10x
5. Two numbers have a sum of 20. Their product is 64. Find the numbers.
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6. The product of two consecutive odd integers is 7 more than their sum. Find the integers.
7. The length of a rectangle is 5 feet more than 3 times the width. The area is 42 square
feet. Find the dimensions.
8. One leg of a right triangle is 2 meters more than twice the other. The hypotenuse is 13
meters. Find the lengths of the two legs.
9. A ball is thrown into the air with an upward velocity of 40 feet per second from a building
that is 24 feet high. The equation that gives the height of the ball above the ground at time
t is h = 24 + 40t − 16t2 .
(a) At what time(s) will the ball be 40 feet above the ground?
(b) When will the ball hit the ground?
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