document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84093>Question 84093</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi Everyone,<BR>\n" );
document.write( "I am supposed to factor the following polynomials completely:\r<BR>\n" );
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document.write( "(a) 14x^2-20x+6  & (b) -3s^2-10s+8\r<BR>\n" );
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document.write( "Could someone please help me understand what it is I am supposed to do here? Please, 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 #60536 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=60536\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You're supposed to find the roots of the equations. Since the<BR>\n" );
document.write( "largest exponent is 2 (x^2), there are 2 roots in each case.<BR>\n" );
document.write( "The roots are values for the unknown that make the equation 0.<BR>\n" );
document.write( "Say the roots are r1 and r2, then<BR>\n" );
document.write( "(x - r1)(x - r2) = 0<BR>\n" );
document.write( "If you then make x = r1,<BR>\n" );
document.write( "(r1 - r1)(r1 - r2) = 0 this is true<BR>\n" );
document.write( "If you make x = r2, then<BR>\n" );
document.write( "(r2 - r1)(r2 - r2) = 0 this is true also<BR>\n" );
document.write( "How do you find the roots? Use the so-called quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 14<BR>\n" );
document.write( "b = -20<BR>\n" );
document.write( "c = +6<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-20%29+%2B-+sqrt%28+%28-20%29%5E2-4%2A14%2A6+%29%29%2F%282%2A14%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-20%29+%2B-+sqrt%28+%28-20%29%5E2-4%2A14%2A6+%29%29%2F%282%2A14%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2820+%2B-+sqrt%28400+-+336%29%29%2F28+ ALIGN=MIDDLE  ALT=\"x+=+%2820+%2B-+sqrt%28400+-+336%29%29%2F28+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2820+%2B-+sqrt%2864%29%29%2F28+ ALIGN=MIDDLE  ALT=\"x+=+%2820+%2B-+sqrt%2864%29%29%2F28+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2820+%2B+8%29+%2F+28 ALIGN=MIDDLE  ALT=\"x+=+%2820+%2B+8%29+%2F+28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2820+-+8%29+%2F+28 ALIGN=MIDDLE  ALT=\"x+=+%2820+-+8%29+%2F+28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1 ALIGN=MIDDLE  ALT=\"x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2F7 ALIGN=MIDDLE  ALT=\"x+=+3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, your factors are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+1%29%28x+-+%283%2F7%29%29 ALIGN=MIDDLE  ALT=\"%28x+-+1%29%28x+-+%283%2F7%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Do these multiplied together give you the original equation?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+1%29%28x+-+%283%2F7%29%29+=+x%5E2+-%2810%2F7%29x+%2B+3%2F7 ALIGN=MIDDLE  ALT=\"%28x+-+1%29%28x+-+%283%2F7%29%29+=+x%5E2+-%2810%2F7%29x+%2B+3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying both sides by 14,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2A%28x+-+1%29%28x+-+%283%2F7%29%29+=+14x%5E2+-+20x+%2B+6 ALIGN=MIDDLE  ALT=\"14%2A%28x+-+1%29%28x+-+%283%2F7%29%29+=+14x%5E2+-+20x+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, 1 and 3/7 are the factors.<BR>\n" );
document.write( "The other equation is factored in the same manner </SPAN>\n" );
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