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Unformatted text preview: Final Review Solutions Math 112 Fall 2008 1. Simplify x 2 y 3 z 2 xy 2 x 4 2 x 10 y 10 z 4 2. Simplify the following 3 r 32 a 12 b 10 c 11 2 a 4 b 3 c 3 3 r 4 b c 2 3. Rewrite the expression using rational exponents rather than radicals. Simplify as much as possible. 3 6 x 4 2 x 2 2 7 / 12 3 1 / 3 x 5 / 6 4. Determine the symmetries of the following: xy = y 2 + 2 It is symmetric about the origin only. 5. Factor 6 x 3 + 7 x 2 5 x x (3 x + 2)(2 x 1) 6. Simplify 5 2 x + 2 3 x 2 x + 2 x + 1 3(3 x 1)( x 2) 2 x ( x + 1)( x 1) 1 2 7. Simplify the following a x 2 + x a 2 a 2 ax + x 2 a + x a 2 x 2 8. Find the equation of the line through the point (1 , 2) and perpendicular to the line through the points ( 1 , 1) and (2 , 3). y = 3 4 x 11 4 9. Determine the center and radius of the circle given by the equation 4 x 2 8 x + 4 y 2 + 16 y + 4 = 0 (1 , 2) r = 2 10. Solve the following x 6 10 x 4 + 24 x 2 = 0 x = 0 , 2 , 6 11. The sum of two positive numbers is onefourth of their sum. The sum of the squares of the two numbers is 50. Find the two numbers....
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 Fall '08
 Carlson
 Algebra, Radicals, Exponents

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