# hw 1 - silva (jrs4378) HW 01 gualdani (56455) 1 This...

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Unformatted text preview: silva (jrs4378) HW 01 gualdani (56455) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Rationalize the numerator of x + 3 x 2 x . 1. 1 x ( x + 3 + x 2) 2. 5 x x + 3 x 2 3. 5 x ( x + 3 x 2) 4. x x + 3 + x 2 5. 5 x ( x + 3 + x 2) correct Explanation: By the difference of squares, ( x + 3 x 2)( x + 3 + x 2) = ( x + 3) 2 ( x 2) 2 = 5 . Thus, after multiplying both the numerator and the denominator in the given expression by x + 3 + x 2 , we obtain 5 x ( x + 3 + x 2) . 002 10.0 points Simplify the expression parenleftBig xy- 3 z parenrightBig 6 parenleftBig y 2 x 1 / 3 z- 2 parenrightBig 12 as much as possible, leaving no negative ex- ponents and no radicals. 1. x 2 y 6 z 21 2. x 10 y 42 z 27 correct 3. x 10 z 27 y 42 4. x 10 y 42 z 27 5. x 10 y 6 z 21 Explanation: By the Laws of Exponents parenleftBig xy- 3 z parenrightBig 6 = x 6 y 18 z 3 , while parenleftBig y 2 x 1 / 3 z- 2 parenrightBig 12 = y 24 z 24 x 4 . Consequently, the given expression can be rewritten as x 6 y 18 z 3 x 4 y 24 z 24 = x 10 y 42 z 27 . 003 10.0 points Simplify the rational expression 10 x 8 x + 16 80 8 x 2 + 16 x + 5 x as much as possible. 1. 5 4 x ( x + 3) 2. 5 4 parenleftBig x + 4 x + 2 parenrightBig correct 3. 5 2 x parenleftBig 2 x + 4 x + 4 parenrightBig 4. 5 4 parenleftBig x + 2 x + 4 parenrightBig 5. 5 2 x parenleftBig x + 4 x + 2 parenrightBig silva (jrs4378) HW 01 gualdani (56455) 2 Explanation: Factoring and bringing to a common de- nominator we get 5 braceleftbigg 2 x 8( x + 2) 16 8 x ( x + 2) + 1 x bracerightbigg = 5 braceleftbigg 2 x 2 16 + 8( x + 2) 8 x ( x + 2) bracerightbigg = 10 x 8 x parenleftbigg x + 4 x + 2 parenrightbigg . Thus after simplification the given rational expression becomes 5 4 parenleftbigg x + 4 x + 2 parenrightbigg . 004 10.0 points Write the expression ( x + 4) 1 / 5 1 2 x ( x + 4)- 4 / 5 as a single fraction containing only positive exponents. 1. x + 8 2( x + 4) 4 / 5 correct 2. x + 2 ( x + 4) 5 / 4 3. 2 x + 8 ( x + 4) 4 / 5 4. x + 8 2( x + 4) 5 / 4 5. x + 2 2( x + 4) 4 / 5 6. 2 x + 8 ( x + 4) 5 / 4 Explanation: Bringing the expression to a common de- nominator, we see that ( x + 4) 1 / 5 1 2 x ( x + 4)- 4 / 5 = 2( x + 4) x 2( x + 4) 4 / 5 = x + 8 2( x + 4) 4 / 5 . 005 10.0 points Simplify the expression f ( x ) = 2 + 6 x 4 1 + 15 parenleftBig x x 2 16 parenrightBig as much as possible. 1. f ( x ) = 2 parenleftBig x + 4 x + 16 parenrightBig correct 2. f ( x ) = x 4 2 x 16 3. f ( x ) = 2 parenleftBig x 4 x + 16 parenrightBig 4. f ( x ) = 2 parenleftBig x + 4 2 x + 16 parenrightBig 5. f ( x ) = x + 4 x 16 6. f ( x ) = x 4 x 16 Explanation: After bringing the numerator to a common denominator it becomes...
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## hw 1 - silva (jrs4378) HW 01 gualdani (56455) 1 This...

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