document.write( "Question 849752: \"find three polynomial functions of different degrees such that each one has zeros at -2, 1 and 3 (and nowhere else).\"\r
\n" ); document.write( "\n" ); document.write( "I found one polynomial function by doing (x+2)(x-1)(x-3) - it came out as x^3-2x^2-5x+6 ; I checked it and it works. But I don't know how to go about finding two other polynomial functions. \n" ); document.write( "

Algebra.Com's Answer #511715 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
You could make one zero have a multiplicity of 2. So for instance, instead of just having the factor \"(x+2)\", you could have \"(x+2)^2\"\r
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\n" ); document.write( "\n" ); document.write( "Expanding out (x+2)^2(x-1)(x-3) will give you a polynomial of degree 4 that has the roots -2, 1 and 3. The root -2 will have a multiplicity of 2. The other two roots will have a multiplicity of 1.\r
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\n" ); document.write( "\n" ); document.write( "Hopefully this helps you in the right direction. If not, then let me know. Thanks. \n" ); document.write( "

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