document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=309477>Question 309477</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you tell me the degree of this polynomial  3^2-2x-7^3+2? Need help. This stuff is new to me.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #221421 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=221421\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%5E2-2x-7%5E3%2B2 ALIGN=MIDDLE  ALT=\"+3%5E2-2x-7%5E3%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2 ALIGN=MIDDLE  ALT=\"3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to 9.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5E3 ALIGN=MIDDLE  ALT=\"7%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to 343.\r<BR>\n" );
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document.write( "This makes your equation equivalent to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+-+2x+-+343+%2B+2 ALIGN=MIDDLE  ALT=\"9+-+2x+-+343+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Combine like terms to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+-+332 ALIGN=MIDDLE  ALT=\"2x+-+332\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Your polynomial simplifies to 2 terms.\r<BR>\n" );
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document.write( "The sum of the exponents in the first term is equal to 1.<BR>\n" );
document.write( "The sum of the exponents in the second term is equal to 0.\r<BR>\n" );
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document.write( "The term with the highest sum of exponents determines the degree of the polynomial.\r<BR>\n" );
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document.write( "The degree of the polynomial is the sum of the exponents in that term.\r<BR>\n" );
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document.write( "The degree of your polynomial is equal to 1.\r<BR>\n" );
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document.write( "The fact that the constants had exponents attached to them doesn't count.\r<BR>\n" );
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document.write( "It's the exponents of the variables in each term of the polynomial that count.\r<BR>\n" );
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document.write( "A constant raised to any power is still a constant.\r<BR>\n" );
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document.write( "The rules for what is a polynomial are reasonably simple, but the determination of whether a polynomial fits those rules can get complicated.\r<BR>\n" );
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document.write( "It's best to simplify the polynomial as much as possible before deciding.\r<BR>\n" );
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document.write( "A polynomial that looks like it violates the rules before simplification may turn out to not violate the rules after simplification.\r<BR>\n" );
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document.write( "The rules are:\r<BR>\n" );
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document.write( "The exponents  of the variables have to be zero or positive only.<BR>\n" );
document.write( "The exponents of the variables have to be integer only.<BR>\n" );
document.write( "The terms in the expression can be added or subtracted from each other only.<BR>\n" );
document.write( "The variables within each term have to be multiplied by each other only.\r<BR>\n" );
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document.write( "Some examples:\r<BR>\n" );
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document.write( "sqrt(x) = x^(1/2) which is not allowed.<BR>\n" );
document.write( "sqrt(x^2) = x which is allowed.<BR>\n" );
document.write( "x/5 = (1/5)*x which is allowed.<BR>\n" );
document.write( "5/x = 5*(1/x) = 5*x^(-1) which is not allowed.<BR>\n" );
document.write( "x*y is allowed.<BR>\n" );
document.write( "x/y is not allowed.\r<BR>\n" );
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document.write( "Dividing a variable by a constant is allowed.<BR>\n" );
document.write( "Dividing a constant by a variable is not.<BR>\n" );
document.write( "Dividing a variable by another variable is not.\r<BR>\n" );
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document.write( "Your expression didn't really violate any rules but they threw you a curve by showing the constants with exponents.\r<BR>\n" );
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document.write( "All you have to remember is that a constant is still a constant regardless of what power it is raised to.\r<BR>\n" );
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document.write( "It's the degree of the variable that counts, not the degree of the constant.\r<BR>\n" );
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document.write( "The degree of a constant is always equal to 0 after you have simplified the constant as much as possible.<BR>\n" );
document.write( "Example;   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2+=+9+=+9%2Ax%5E0 ALIGN=MIDDLE  ALT=\"3%5E2+=+9+=+9%2Ax%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Any variable name can be used to prove the point since any variable raised to the 0 power is equal to 1.\r<BR>\n" );
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document.write( "The degree of a variable without an exponent attached is equal to 1.<BR>\n" );
document.write( "Example:   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+x%5E1 ALIGN=MIDDLE  ALT=\"x+=+x%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Examples of terms and the degree of the term:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E5 ALIGN=MIDDLE  ALT=\"x%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = degree of 5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Ax%5E5 ALIGN=MIDDLE  ALT=\"5%2Ax%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = degree of 5 because the sum of the exponents is equal to 0 + 5.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Ax%5E5%2Ay ALIGN=MIDDLE  ALT=\"5%2Ax%5E5%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" > = degree of 6 because the sum of the exponents is equal to 0 + 5 + 1.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000%5E15%2Ax%5E3%2Ay%5E4%2Az%5E2 ALIGN=MIDDLE  ALT=\"5000%5E15%2Ax%5E3%2Ay%5E4%2Az%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = degree of 9 because the sum of the exponents is equal to 0 + 3 + 4 + 2.\r<BR>\n" );
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