document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=282871>Question 282871</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the question is:find all the zeros of the function.is there a relationship between the number of real zeros and the number of x-intercepts of the graph? explain.f(x)=x^3-4x^2+x-4\r<BR>\n" );
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document.write( "this is what I have so far and I don't know were to go from here.<BR>\n" );
document.write( "(x^3-4x^2)+(x-4)=x^2(x-4)+(x-4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #205338 by </B><A HREF=/tutors/aboutme.mpl?userid=nyc_function><B>nyc_function(2741)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nyc_function><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=nyc_function><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=205338\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the zeros means to find the number(s) that when replaced for the given x in your polynomial function, will create zero for the function.  In other words, we need to find numbers (or maybe just one number) that when used in place of every x in your function, zero is the result.\r<BR>\n" );
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document.write( "We can use synthetic division to find our zero(s).\r<BR>\n" );
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document.write( "See the video clip to learn about synthetic division.\r<BR>\n" );
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document.write( "http://www.youtube.com/watch?v=HY2UylGTDYU\r<BR>\n" );
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document.write( "====================================================\r<BR>\n" );
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document.write( "Back to your question.\r<BR>\n" );
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document.write( "I will use synthetic division on paper until finding one number or group of numbers that will give me a zero remainder.\r<BR>\n" );
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document.write( "List the factors of the leading coefficient and the constant.\r<BR>\n" );
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document.write( "Factor of 1 = 1\r<BR>\n" );
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document.write( "Factors of 4 = 1, 2, and 4\r<BR>\n" );
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document.write( "We now divide the constant's factors by the factor of the leading coefficient.\r<BR>\n" );
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document.write( "±1/1, ±2/1 and ±4/1 = ±1, ±2 and ±4\r<BR>\n" );
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document.write( "After using synthetic division, I found the only zero to be x = 4.\r<BR>\n" );
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document.write( "In other words, if you replace x with 4 in your function, you will get zero on both sides of the equation.\r<BR>\n" );
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document.write( "Why don't you try it?\r<BR>\n" );
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document.write( "0 = (4)^3 - 4(4)^2 + 4 - 4...After doing the math, the right side should also produce zero.\r<BR>\n" );
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document.write( "I'll let you do the math.\r<BR>\n" );
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document.write( "The x-intercept of any function is the location where the graph of the function crosses the x-axis.  So, there is a relationship between the x-intercepts and the zeros.  In fact, the x-intercepts = the roots = the solution = the zeros.  \r<BR>\n" );
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document.write( " </SPAN>\n" );
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