document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83530>Question 83530</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I NEED HELP ON POLYNOMIALS. FOR FINALS WE NEED TO KNOW WHAT IS THE DEGREE AND NAME OF IT. MY FIRST PROBLEM SAYS: 5X^2 - 3X^2. I NEED YOU TO HELP ME FIGURE OUT THE DEGREE, THE NAME OF THE DEGREE, AND THE NAME BY TERM. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #60074 by </B><A HREF=/tutors/aboutme.mpl?userid=praseenakos@yahoo.com><B>praseenakos@yahoo.com(507)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=praseenakos@yahoo.com><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=praseenakos@yahoo.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=60074\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  A polynomial is an algebraic expression that is a sum of terms, where each term contains only variables with whole number exponents and integer coefficients.\r<BR>\n" );
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document.write( "Example:  The following expressions are all considered polynomials:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 4x + 7 \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 2x – 7\r<BR>\n" );
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document.write( "The following are NOT polynomials:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28x%5E3+-4%29 ALIGN=MIDDLE  ALT=\"+sqrt%28x%5E3+-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A polynomial can have any number of terms (“poly” means “many”). We have special names for polynomials that have one, two, or three terms:\r<BR>\n" );
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document.write( "A monomial has one term (“mono” means “one”). The following are monomials:\r<BR>\n" );
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document.write( "x,   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E4 ALIGN=MIDDLE  ALT=\"3x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ,    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3 ALIGN=MIDDLE  ALT=\"2x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > etc.\r<BR>\n" );
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document.write( "A binomial has two terms:\r<BR>\n" );
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document.write( "x + 1,   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2+ ALIGN=MIDDLE  ALT=\"5x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > – 3x\r<BR>\n" );
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document.write( "A trinomial has three terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+%2B+2x%5E3+ ALIGN=MIDDLE  ALT=\"x%5E4+%2B+2x%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > – 3x       ,   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2 ALIGN=MIDDLE  ALT=\"2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > – 4x + 1\r<BR>\n" );
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document.write( "The degree of an individual term in a polynomial is the sum of powers of all the variables in that term. \r<BR>\n" );
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document.write( "Examples: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x%5E+3+ ALIGN=MIDDLE  ALT=\"+2x%5E+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  here...Degree = 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E4 ALIGN=MIDDLE  ALT=\"3x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Degree = 4\r<BR>\n" );
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document.write( "x ... degree = 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2y%5E5 ALIGN=MIDDLE  ALT=\"3x%5E2y%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Degree = 7 (because 2 + 5 = 7)\r<BR>\n" );
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document.write( "37 here  Degree = 0, because here you dont have a vairable<BR>\n" );
document.write( "Remember that  degree of a constat term is always zero.\r<BR>\n" );
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document.write( "The degree of the entire polynomial is the degree of the highest-degree term that it contains, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+ ALIGN=MIDDLE  ALT=\"x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 2x – 7 is a second-degree trinomial, \r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+%96+7x%5E3 ALIGN=MIDDLE  ALT=\"x%5E4+%96+7x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  is a fourth-degree binomial. \r<BR>\n" );
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document.write( "Now come back to your question...it is...\r<BR>\n" );
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document.write( "5X^2 - 3X^2. I NEED YOU TO HELP ME FIGURE OUT THE DEGREE, THE NAME OF THE DEGREE, AND THE NAME BY TERM.\r<BR>\n" );
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document.write( "In this question you have two terms...they are 5x^2 and 3x^2\r<BR>\n" );
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document.write( "Degree of both the terms is 2.\r<BR>\n" );
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document.write( "So this is a second degree polynomial.\r<BR>\n" );
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document.write( "But here you can simplyfy the given expression(since both the terms are of same degree) as follow.....\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2+-+3x%5E2+ ALIGN=MIDDLE  ALT=\"5x%5E2+-+3x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x%5E2+ ALIGN=MIDDLE  ALT=\"+2x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here we got a single term.....so we can say that the given polynomial is a second degree monomial(since there is only one term)<BR>\n" );
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document.write( "Hope you  found the explanation useful.\r<BR>\n" );
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document.write( "Regards.\r<BR>\n" );
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document.write( "Praseena.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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