document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=350163>Question 350163</A>: <I><SPAN STYLE=\"word-break: break-all;\"> factor completely     3x^5-12x^4+21x^3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #250314 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=250314\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> factor completely     3x^5-12x^4+21x^3\r<BR>\n" );
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document.write( "find the greatest common factor of each of the 3 terms of this trinomial (polynomial with 3 terms) and factor it out\r<BR>\n" );
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document.write( "that is 3x^3 since the coefficients 3, -12, and 21 are all divisible by 3, and x^5, x^4, and x^3 are all divisible by x^3\r<BR>\n" );
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document.write( "3x^3(x^2 - 4x + 7)<BR>\n" );
document.write( "now see if x^2 - 4x + 7 can be factored\r<BR>\n" );
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document.write( "set the trinomial equal to 0, now it is a quadratic equation of<BR>\n" );
document.write( "the form ax^2 + bx + c = 0, where a = 1, b = -4, and c = 7<BR>\n" );
document.write( "use the discriminant of the quadratic equation to determine if there is solutions among real numbers (any number that is not imaginary, does not involve the imaginary number i, where i is square root of -1)\r<BR>\n" );
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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;\" >\r<BR>\n" );
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document.write( "disciminant b^2 - 4ac = -4^2 - 4 * 1 * 7 = 16 - 28 = -12<BR>\n" );
document.write( "discriminant is negative, no solutions among real numbers<BR>\n" );
document.write( "x^2 - 4x + 7 can not be factored using real numbers\r<BR>\n" );
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document.write( "3x^5-12x^4+21x^3 factored completely is 3x^3(x^2 - 4x + 7) without going into complex numbers (numbers of form a + bi where a and b are real numbers and i is the square root of -1)\r<BR>\n" );
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