document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164733>Question 164733</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor 10x^2-21x-10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121416 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=121416\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> answer is:<BR>\n" );
document.write( "(2x-5) * (5x+2) = 0<BR>\n" );
document.write( "multiplying out using FOIL, you get<BR>\n" );
document.write( "First = 2x * 5x = 10x<BR>\n" );
document.write( "Outer = 2x * 2 = 4x<BR>\n" );
document.write( "Inner = -5 * 5x = -25x<BR>\n" );
document.write( "Last = -5 * 2 = -10<BR>\n" );
document.write( "adding all up together, you get<BR>\n" );
document.write( "10x^2 - 21x - 10<BR>\n" );
document.write( "which is your original equation.<BR>\n" );
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document.write( "original equation is 10x^2 - 21x - 10<BR>\n" );
document.write( "a = 10<BR>\n" );
document.write( "b = -21<BR>\n" );
document.write( "c = -10<BR>\n" );
document.write( "b^2 - 4ac = 841 which has an integral square root (29) which indicates the roots are integers.<BR>\n" );
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document.write( "since you know that the roots are integers, then you need to find the right combination of factors of a and c which will provide the answer.<BR>\n" );
document.write( "a = 10 has factors of 10 & 1, or 5 & 2.<BR>\n" );
document.write( "c = -10 has factors of 10 & 1, or 5 & 2 also if you neglect the signs for now.<BR>\n" );
document.write( "you do cross multiplies and adds to see if the middle factor of b will be correct (ax^2 + bx + c).<BR>\n" );
document.write( "using 10 & 1 for a, and 10 & 1 for c, we get 10*10 & 1*1 not equal to -21<BR>\n" );
document.write( "we also get 10*1 & 10*1 still not equal to -21.<BR>\n" );
document.write( "an a factor of 10 & 1, with a c factor of 10 & 1 is clearly no good.<BR>\n" );
document.write( "same with 10 & 1 for a, and 5 & 2 for c.<BR>\n" );
document.write( "you get 10*5 & 1*2, or 10*2 & 5*1, neither of which will add or subtract to equal -21.<BR>\n" );
document.write( "5 & 2 for a, and 5 & 2 for c, come out as follows:<BR>\n" );
document.write( "5*2 & 2*5 give 10 & 10 which don't add or subtract to be = to -21.<BR>\n" );
document.write( "5*5 & 2*2 give 25 & 4 which DO equal to -21 when 2*2 is positive and 5*5 is negative.<BR>\n" );
document.write( "so the a factors are 5 and 2, and the c factors are 5 and 2, in a specific combination that cross multiplies to be - (5*5) + (2*2).<BR>\n" );
document.write( "this comes out to be (5x+2) * (2x-5).<BR>\n" );
document.write( "using FOIL to multiply these factors together gets<BR>\n" );
document.write( "First (F) = 5x*2x = 10x^2<BR>\n" );
document.write( "Outer (O) = 5x * -5 = -25x<BR>\n" );
document.write( "Inner (I) = 2*2x = +4x<BR>\n" );
document.write( "Last (L) = 2*-5 = -10<BR>\n" );
document.write( "this was already done up above and shown to be correct.<BR>\n" );
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document.write( "i did use the quadratic equation but didn't come up with the answer directly.  not sure why.  something for me to research.<BR>\n" );
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document.write( "hope this is good enough for what you need.\r<BR>\n" );
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