Q4SOL - MAP 103: Proficiency Algebra, Quiz #4, Fall 2009...

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Unformatted text preview: MAP 103: Proficiency Algebra, Quiz #4, Fall 2009 SOLUTIONS 1. Factorize completely: (a) p ( x ) = 8 x 2 + 8 x + 2 Sol. p ( x ) = 8 x 2 + 8 x + 2 = 2(4 x 2 + 4 x + 1) = 2(2 x + 1)(2 x + 1) = 2(2 x + 1) 2 (b) q ( x ) = ( x 2- 1) 4- ( x 2- 1) 2 Sol. Set A = x 2- 1 , then q ( x ) = ( x 2- 1) 4- ( x 2- 1) 2 = A 4- A 2 = A 2 ( A 2- 1) = A 2 ( A- 1)( A + 1) = ( x 2- 1) 2 ( x 2- 1- 1)( x 2- 1 + 1) = x 2 ( x 2- 1) 2 ( x 2- 2) = x 2 [( x- 1)( x + 1)] 2 ( x- 2)( x + 2) 2. Use the Rational Root Theorem to find all the roots of the polynomial p ( x ) = x 3- 6 x 2 +11 x- 6 . Sol. By the rational root test, we find the possible roots are r = 6 1 = { 1 2 3 6 } . By the remainder theorem, we find p (1) = p (2) = p (3) = 0 . Hence, the roots are r 1 = 1 ,r 2 = 2 ,r 3 = 3 . 3. Find the quotient and remainder (if any) upon long division: x 6- 5 x 4 + x 2 x 2- 1 . Sol. In each case, we need place holders. Thus, we are dividing the following: x 6 + 0 x 5- 5 x 4 + 0 x 3 + x 2 + 0 x + 0 x 2...
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This note was uploaded on 04/18/2010 for the course MAP 103 taught by Professor Staff during the Fall '08 term at SUNY Stony Brook.

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Q4SOL - MAP 103: Proficiency Algebra, Quiz #4, Fall 2009...

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