document.write( "Question 44650This question is from textbook
\n" ); document.write( ": Find the polynomial f(x) of degree three that zeroes at 1, 2, and 4 such that f(0)=-16.\r
\n" ); document.write( "\n" ); document.write( "Thank you! \n" ); document.write( "

Algebra.Com's Answer #29691 by adamchapman(301) $\"\"$ $\"About$

You can put this solution on YOUR website!
We know that:
\n" ); document.write( " $\"f%281%29=0\"$ ,
\n" ); document.write( " $\"f%282%29=0\"$ ,
\n" ); document.write( " $\"f%284%29=0\"$ .
\n" ); document.write( "And the Highest power of x is cubed $\"x%5E3\"$
\n" ); document.write( "This step is pretty simple just put in brackets (x-a) where a is the value of x where f(x)=0 (i.e. f(a)=0):
\n" ); document.write( " $\"f%28x%29=b%28x-1%29%28x-2%29%28x-4%29\"$ (Don't worry, the value of \"b\" is about to become clearer).
\n" ); document.write( "We also know that when x=0, f(x)=-16. Try to find the value of f(0) with our previous equation:
\n" ); document.write( " $\"f%280%29=b%28-1%29%28-2%29%28-4%29=16\"$
\n" ); document.write( " $\"-8b=-16\"$
\n" ); document.write( "so b=2.
\n" ); document.write( "Now we can write the function:
\n" ); document.write( " $\"f%28x%29=2%28x-1%29%28x-2%29%28x-4%29\"$
\n" ); document.write( "here's the graph of y=f(x):
\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-6%2C+5%2C+-20%2C+10%2C+2%28x-1%29%28x-2%29%28x-4%29%29+\"$
\n" ); document.write( "I hope this helps.
\n" ); document.write( "P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk
\n" ); document.write( "Adam\r
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