document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190673>Question 190673</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321233832/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> If a fourth degree polynomial is multiplied by a third degree polynomial, what is the degree of the product? Explain your reasoning and provise examples.<BR>\n" );
document.write( "Thank You </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143149 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=143149\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The product of a fourth degree polynomial and a third degree polynomial is a 7th degree polynomial (just add the two degrees). Why is this the case? Remember, when you multiply variables with common bases, you add the exponents. Since the degree of a polynomial is just the largest exponent, you're really just adding the degrees when you multiply\r<BR>\n" );
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document.write( "Example: Let's multiply the fourth degree binomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4%2B3x ALIGN=MIDDLE  ALT=\"x%5E4%2B3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the third degree binomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-10 ALIGN=MIDDLE  ALT=\"x%5E3-10\"   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=%28x%5E4%2B3x%29%28x%5E3-10%29 ALIGN=MIDDLE  ALT=\"%28x%5E4%2B3x%29%28x%5E3-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "Now let's FOIL the expression.\r<BR>\n" );
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document.write( "Remember, when you FOIL an expression, you follow this procedure:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%28x%5E4%29%2B3x%29%28highlight%28x%5E3%29-10%29 ALIGN=MIDDLE  ALT=\"%28highlight%28x%5E4%29%2B3x%29%28highlight%28x%5E3%29-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">F</font>irst terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E4%29%2A%28x%5E3%29=x%5E7 ALIGN=MIDDLE  ALT=\"%28x%5E4%29%2A%28x%5E3%29=x%5E7\"   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=%28highlight%28x%5E4%29%2B3x%29%28x%5E3%2Bhighlight%28-10%29%29 ALIGN=MIDDLE  ALT=\"%28highlight%28x%5E4%29%2B3x%29%28x%5E3%2Bhighlight%28-10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">O</font>uter terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E4%29%2A%28-10%29=-10%2Ax%5E4 ALIGN=MIDDLE  ALT=\"%28x%5E4%29%2A%28-10%29=-10%2Ax%5E4\"   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=%28x%5E4%2Bhighlight%283x%29%29%28highlight%28x%5E3%29-10%29 ALIGN=MIDDLE  ALT=\"%28x%5E4%2Bhighlight%283x%29%29%28highlight%28x%5E3%29-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">I</font>nner terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Ax%29%2A%28x%5E3%29=3%2Ax%5E4 ALIGN=MIDDLE  ALT=\"%283%2Ax%29%2A%28x%5E3%29=3%2Ax%5E4\"   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=%28x%5E4%2Bhighlight%283x%29%29%28x%5E3%2Bhighlight%28-10%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E4%2Bhighlight%283x%29%29%28x%5E3%2Bhighlight%28-10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">L</font>ast terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Ax%29%2A%28-10%29=-30%2Ax ALIGN=MIDDLE  ALT=\"%283%2Ax%29%2A%28-10%29=-30%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "---------------------------------------------------\r<BR>\n" );
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document.write( "So we have the terms: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E7 ALIGN=MIDDLE  ALT=\"x%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10%2Ax%5E4 ALIGN=MIDDLE  ALT=\"-10%2Ax%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax%5E4 ALIGN=MIDDLE  ALT=\"3%2Ax%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-30%2Ax ALIGN=MIDDLE  ALT=\"-30%2Ax\"   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=x%5E7-10%2Ax%5E4%2B3%2Ax%5E4-30%2Ax ALIGN=MIDDLE  ALT=\"x%5E7-10%2Ax%5E4%2B3%2Ax%5E4-30%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now add every term listed above to make a single expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E7-7%2Ax%5E4-30%2Ax ALIGN=MIDDLE  ALT=\"x%5E7-7%2Ax%5E4-30%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E4%2B3x%29%28x%5E3-10%29 ALIGN=MIDDLE  ALT=\"%28x%5E4%2B3x%29%28x%5E3-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOILs to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E7-7%2Ax%5E4-30%2Ax ALIGN=MIDDLE  ALT=\"x%5E7-7%2Ax%5E4-30%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E4%2B3x%29%28x%5E3-10%29=x%5E7-7x%5E4-30%2Ax ALIGN=MIDDLE  ALT=\"%28x%5E4%2B3x%29%28x%5E3-10%29=x%5E7-7x%5E4-30%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Notice how the degree of the final answer is 7. So this confirms the original claim. </SPAN>\n" );
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