document.write( "Question 71792: someone please show or explain the easiest way to understand this\r
\n" ); document.write( "\n" ); document.write( "Find the polynomial with leading coefficient 1 and degree 3 that has -1, 1, and 3 as roots.\r
\n" ); document.write( "\n" ); document.write( "Possible answers:\r
\n" ); document.write( "\n" ); document.write( "x3 - 3x2 -x +3
\n" ); document.write( ".x3 -3x2 + x -3
\n" ); document.write( ".x3 +3x2 +x +3
\n" ); document.write( ".x3 + 3x2 +x +3\r
\n" ); document.write( "\n" ); document.write( "Thanks to anyone who can help me \n" ); document.write( "
Algebra.Com's Answer #51328 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
Find the polynomial with leading coefficient 1 and degree 3 that has -1, 1, and 3 as roots
\n" ); document.write( "----------
\n" ); document.write( "If 1 is a root, x=1, or x-1=0
\n" ); document.write( "If -1 is a root, x=-1 or x+1=0
\n" ); document.write( "If 3 is a root, x=3, or x-3=0
\n" ); document.write( "-------
\n" ); document.write( "Multiply those three results and you get
\n" ); document.write( "(x-1)(x+1)(x-3)=0
\n" ); document.write( "That is the polynomial you want.
\n" ); document.write( "If you multiply it out you get:
\n" ); document.write( "=(x^2-1)(x-3)
\n" ); document.write( "=x^3-3x^2-x+3
\n" ); document.write( "If you are asked for the equation that has those roots and leading coefficient
\n" ); document.write( "of 1 you write: y=x^3-3x^2-x+3
\n" ); document.write( "-------
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "
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