document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151967>Question 151967</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.	Using one of the laws of exponents, prove that any number raised to the power 0 is 1.<BR>\n" );
document.write( "2.	Using FOIL, simplify the expression \"(3x + 2)(3x - 2)\".  Show that a particular factoring formula leads to the same answer. <BR>\n" );
document.write( "3.	If a fourth-degree polynomial is multiplied by a third-degree polynomial, what is the degree of the product? Explain your reasoning and provide examples to support your explanation. <BR>\n" );
document.write( "4.	Think of a condition under which the product of any two binomials is a binomial. You can support your answer with the help of one of the identities of factorization of polynomials.<BR>\n" );
document.write( "5.	(i) Is \"12.5555…\" a rational or irrational number?  Explain.<BR>\n" );
document.write( "(ii) Is \"2.1273685…\" a rational or irrational number?  Explain.<BR>\n" );
document.write( "(iii) Is \"548/799\" a rational or irrational number?  Explain.  <BR>\n" );
document.write( "(iv) Simplify \"(5 + 3i)(5 - 3i)\".  Is the result real, complex, or both?  Explain.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111721 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=111721\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Using one of the laws of exponents, prove that any number raised to the power 0 is 1.<BR>\n" );
document.write( "n^x/n^x = 1 because anything, except zero, divided by itself is one.<BR>\n" );
document.write( "But n^x/n^x = n^(x-x) = n^0 by the division law of exponents.<BR>\n" );
document.write( "Therefore n^0 must equal 1 for all n that is not equal to zero.<BR>\n" );
document.write( "-----------------------------\r<BR>\n" );
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document.write( "2. Using FOIL, simplify the expression \"(3x + 2)(3x - 2)\".<BR>\n" );
document.write( "F: 3x*3x = 9x^2<BR>\n" );
document.write( "O: 3x*-2 = -6x<BR>\n" );
document.write( "I: 2*3x = 6x<BR>\n" );
document.write( "L: 2*-2 = -4<BR>\n" );
document.write( "Combine to get: 9x^2 -4<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( " Show that a particular factoring formula leads to the same answer. <BR>\n" );
document.write( "(a+b)(a-b) = a^2 - b^2 is the form for the difference of squares.<BR>\n" );
document.write( "In your problem a = 3x and b = 2<BR>\n" );
document.write( "So you have (3x+2)(3x-2) = (3x)^2-2^2 = 9x^2-4<BR>\n" );
document.write( "-------------------------------------------------<BR>\n" );
document.write( "3. If a fourth-degree polynomial is multiplied by a third-degree polynomial, what is the degree of the product?<BR>\n" );
document.write( "seven<BR>\n" );
document.write( "Explain your reasoning and provide examples to support your explanation.<BR>\n" );
document.write( "(x^4-1)(x^3-1) = x^7-x^4-x^3+1<BR>\n" );
document.write( "---------------------------------------- <BR>\n" );
document.write( "4. Think of a condition under which the product of any two binomials is a binomial. You can support your answer with the help of one of the identities of factorization of polynomials.<BR>\n" );
document.write( "(a+b)(a-b) = a^2-b^2<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "5. (i) Is \"12.5555…\" a rational or irrational number? Explain.<BR>\n" );
document.write( "rational because is has a repeating decimal form.<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "(ii) Is \"2.1273685…\" a rational or irrational number? Explain.<BR>\n" );
document.write( "It appears to have a non-repeating decimal form so it is irrational.<BR>\n" );
document.write( "-----------------\r<BR>\n" );
document.write( "\n" );
document.write( "(iii) Is \"548/799\" a rational or irrational number? Explain. <BR>\n" );
document.write( "rational because it is the ratio of two integers.<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "(iv) Simplify \"(5 + 3i)(5 - 3i)\". Is the result real, complex, or both? Explain.<BR>\n" );
document.write( " = 5^2 - (3i)^2 = 25 +9 = 34 which is rational.<BR>\n" );
document.write( "=================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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