document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=594419>Question 594419</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.	Find all roots of x3 + 2x2 + 2x + 1. Hint: Find the rational one(s) first.<BR>\n" );
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document.write( " B.  \r<BR>\n" );
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document.write( " C.  \r<BR>\n" );
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document.write( " D.  \r<BR>\n" );
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document.write( "2.	Solve 2x = 5x2 for x.<BR>\n" );
document.write( " A. 2.322\r<BR>\n" );
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document.write( " B. 0 and 2.322\r<BR>\n" );
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document.write( " C. 0 and 0.431\r<BR>\n" );
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document.write( " D. 0.431\r<BR>\n" );
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document.write( "3.	Which of the following is not a property of logarithms?<BR>\n" );
document.write( " A.  \r<BR>\n" );
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document.write( " B.  \r<BR>\n" );
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document.write( " C.  \r<BR>\n" );
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document.write( " D.  \r<BR>\n" );
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document.write( "4.	A falling object has velocity 37(1 &#8722; e–0.4t) meters per second after t seconds of free fall. Which of the following statements is true?<BR>\n" );
document.write( " A. Its initial velocity was 0 meters per second and its velocity after 10 seconds is –12.2 meters per second.<BR>\n" );
document.write( " B. Its initial velocity was –1 meter per second and its velocity after 10 seconds is –36.3 meters per second.<BR>\n" );
document.write( " C. Its initial velocity was 0 meters per second and its velocity after 10 seconds is 36.3 meters per second.<BR>\n" );
document.write( " D. Its initial velocity was 1 meter per second and its velocity after 10 seconds is 12.2 meters per second.\r<BR>\n" );
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document.write( "5.	How many roots does x6 = 3x5 + 1 have?<BR>\n" );
document.write( " A. 6\r<BR>\n" );
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document.write( " B. 5\r<BR>\n" );
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document.write( " C. 11\r<BR>\n" );
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document.write( " D. 1\r<BR>\n" );
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document.write( "6.	If 2 &#8722; i is a root of 3x3 &#8722; 11x2 + 11x + 5, then what are its other roots?<BR>\n" );
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document.write( " C.  \r<BR>\n" );
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document.write( "7.	On which interval does the Intermediate Value Theorem guarantee that the polynomial x4 + 7x2 &#8722; 9x &#8722; 1 has a root?<BR>\n" );
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document.write( "8.	If 1 and –6 are two of the roots of 6x4 + 31 x3 &#8722; 33x2 &#8722; 16x + 12, then what are the other two?<BR>\n" );
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document.write( "9.	Which of these graphs could be the graph of y = ex + 1?<BR>\n" );
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document.write( " B.  \r<BR>\n" );
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document.write( " C.  \r<BR>\n" );
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document.write( " D.  \r<BR>\n" );
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document.write( "10.	Why do we use the Intermediate Value and Bisection Theorems to find only the irrational roots of polynomials?<BR>\n" );
document.write( " A. It is the only method available for finding irrational roots of any polynomial.\r<BR>\n" );
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document.write( " B. The Rational Roots Theorem is better for finding the rational roots.\r<BR>\n" );
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document.write( " C. Those theorems are unable to find rational roots.\r<BR>\n" );
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document.write( " D. No polynomial has rational roots.\r<BR>\n" );
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document.write( "11.	A population of 2000 snakes is released into a marshland and grows according to the formula P = 2000 • 1.5t, where t is the number of months after the release. Find the population 10 months after the release.<BR>\n" );
document.write( " A. 63,246\r<BR>\n" );
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document.write( " B. 115,330\r<BR>\n" );
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document.write( " C. 5.9 x 1034\r<BR>\n" );
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document.write( " D. 30,000\r<BR>\n" );
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document.write( "12.	Write  in terms of ln a, ln b, and ln c. You may assume that all variables are positive.<BR>\n" );
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document.write( "13.	Which of these is the result of (x5 &#8722; x3 + 2x2 &#8722; 9x + 5) ÷ (x + 2)?<BR>\n" );
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document.write( "14.	Evaluate  .<BR>\n" );
document.write( " A. 2\r<BR>\n" );
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document.write( " B. 4\r<BR>\n" );
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document.write( " C. ¼\r<BR>\n" );
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document.write( " D. ½\r<BR>\n" );
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document.write( "15.	Find the point (x, y) on the parabola y = 9 &#8722; x2 such that the shaded rectangle in the figure below has area 20 square units.<BR>\n" );
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document.write( " B.  \r<BR>\n" );
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document.write( "16.	Solve ln t = log 50 for t.<BR>\n" );
document.write( " A. t = 5.47\r<BR>\n" );
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document.write( " B. t = 8166.3\r<BR>\n" );
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document.write( " C. t = 13.6\r<BR>\n" );
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document.write( " D. t = 50\r<BR>\n" );
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document.write( "17.	Which of the following is the conclusion you can draw using Descartes' Rule of Signs applied to 2x4 &#8722; 6x3 + x2 + 7x &#8722; 4?<BR>\n" );
document.write( " A. Zero is not a root.<BR>\n" );
document.write( "There are either 1 or 3 positive real roots.<BR>\n" );
document.write( "There are 3 negative real roots.<BR>\n" );
document.write( "There are either 0 or 2 complex roots.<BR>\n" );
document.write( " B. Zero is not a root.<BR>\n" );
document.write( "There are either 1 or 3 positive real roots.<BR>\n" );
document.write( "There are 3 negative real roots.<BR>\n" );
document.write( "No information is available about the number of complex roots.<BR>\n" );
document.write( " C. Zero is not a root.<BR>\n" );
document.write( "There are either 1 or 3 positive real roots.<BR>\n" );
document.write( "There is 1 negative real root.<BR>\n" );
document.write( "There are either 0 or 2 complex roots. <BR>\n" );
document.write( " D. Zero is not a root.<BR>\n" );
document.write( "There are either 1 or 3 positive real roots.<BR>\n" );
document.write( "There is 1 negative real root.<BR>\n" );
document.write( "No information is available about the number of complex roots.\r<BR>\n" );
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document.write( "18.	Which of these is the remainder when 4x4 &#8722; 5x3 + 9 is divided by x &#8722; 3?<BR>\n" );
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document.write( " B.  \r<BR>\n" );
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document.write( " D.  \r<BR>\n" );
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document.write( "19.	Which of these could be the graph of y = 7x &#8722; 2?<BR>\n" );
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document.write( "20.	Simplify  .<BR>\n" );
document.write( " A.  \r<BR>\n" );
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document.write( " B. 216\r<BR>\n" );
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document.write( " C.  \r<BR>\n" );
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document.write( " D.  is already in simplified form.\r<BR>\n" );
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document.write( "21.	Which of the following is a reason for why the trace function on a graphing calculator can sometimes be better than the Bisection Theorem for finding roots?<BR>\n" );
document.write( " A. The trace function always finds an exact root.\r<BR>\n" );
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document.write( " B. The Intermediate Bisection Theorem applies only to continuous functions, and not all polynomials are continuous.<BR>\n" );
document.write( " C. Some roots aren't surrounded by one positive and one negative value of the polynomial<BR>\n" );
document.write( " D. The Bisection Theorem can't find roots to more than 3 decimal places.\r<BR>\n" );
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document.write( "22.	If a cubic polynomial has roots –5 and 6 &#8722; 2i, what is its third root?<BR>\n" );
document.write( " A. 1 &#8722; 2i\r<BR>\n" );
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document.write( " B. –30 + 10i\r<BR>\n" );
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document.write( " C. 6 + 2i\r<BR>\n" );
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document.write( " D. 5\r<BR>\n" );
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document.write( "23.	Which of the following is a correct description of the expression logbx?<BR>\n" );
document.write( " A. It is the power to which b must be raised to yield x.\r<BR>\n" );
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document.write( " B. It is the xth power of b.\r<BR>\n" );
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document.write( " C. It is the bth power of x.\r<BR>\n" );
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document.write( " D. It is the power to which x must be raised to yield b.\r<BR>\n" );
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document.write( "24.	Which of the following is equal to log6(t + 1) &#8722; log6(t2 &#8722; 1)?<BR>\n" );
document.write( " A. log6(t + 1)\r<BR>\n" );
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document.write( " B. log6t &#8722; log6t2\r<BR>\n" );
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document.write( " C. log6t\r<BR>\n" );
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document.write( " D. –log6(t &#8722; 1)\r<BR>\n" );
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document.write( "25.	Which are upper and lower bounds for the real roots of 3x4 &#8722; 2x3 + x &#8722; 9 = 0?<BR>\n" );
document.write( " A. –3 and –1, 1, and 3\r<BR>\n" );
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document.write( " B. –2 and 2\r<BR>\n" );
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document.write( " C. –2 and –1, 1, and 2\r<BR>\n" );
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document.write( " D. 0 and 3\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #376718 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=376718\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Find all roots of x3 + 2x2 + 2x + 1. Hint: Find the rational one(s) first.<BR>\n" );
document.write( "Hint:  Try the factors of 1.<BR>\n" );
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document.write( "No one's gonna do all these problems.<BR>\n" );
document.write( "Post them separately, you might get some of them.<BR>\n" );
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