document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165419>Question 1165419</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor completely or state that the polynomial is prime.\r<BR>\n" );
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document.write( "25x^2 + 30x - 36\r<BR>\n" );
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document.write( "Find the value of the integer k so that the trinomial is a perfect square trinomial, and write the factored form.\r<BR>\n" );
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document.write( "49y^2 - 42y + k,\r<BR>\n" );
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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 #789967 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=789967\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%5E2%2B30x-36 ALIGN=MIDDLE  ALT=\"25x%5E2%2B30x-36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Spend at most a very little time trying to factor it.  Then look at the discriminant, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "The discriminant in this quadratic is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%5E2-4%2825%29%28-36%29+=+900%2B3600+=+4500 ALIGN=MIDDLE  ALT=\"30%5E2-4%2825%29%28-36%29+=+900%2B3600+=+4500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A quadratic is factorable (over the integers) only if the discriminant is a perfect square.  4500 is not a perfect square, so this quadratic is not factorable.<br><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49y%5E2-42y%2Bk ALIGN=MIDDLE  ALT=\"49y%5E2-42y%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "If this is to be a perfect square trinomial, then it must be of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287y-a%29%5E2 ALIGN=MIDDLE  ALT=\"%287y-a%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287y-a%29%5E2+=+49y%5E2-14ay%2Ba%5E2 ALIGN=MIDDLE  ALT=\"%287y-a%29%5E2+=+49y%5E2-14ay%2Ba%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Since the linear term of the trinomial is -42y, a=3; then a^2 = 3^2 = 9.<br><BR>\n" );
document.write( "ANSWER: k = 9<br><BR>\n" );
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