document.write( "Question 1041569: Please help me graph this problem:\r
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\n" ); document.write( "\n" ); document.write( "Consider the given function.
\n" ); document.write( "f(x)=x^3+2x^2-x-2\r
\n" ); document.write( "\n" ); document.write( "Use the Remainder Theorem to plot all the values of a in the interval [-4, 4] where f(a) = 0.
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Algebra.Com's Answer #656517 by Boreal(15235) $\"\"$ $\"About$

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f(x)=x^3+2x^2-x-2
\n" ); document.write( "Remainder theorem says that if one divides by a number a, the remainder is f(a).
\n" ); document.write( "We want f(a)=0
\n" ); document.write( "synthetic division
\n" ); document.write( "2|1===2===-1====-1
\n" ); document.write( "=1== 4====7====12; f(2)=12
\n" ); document.write( "-2
\n" ); document.write( "==1===0===-1===0
\n" ); document.write( "-2 is a root, so (x+2) is a factor.
\n" ); document.write( "The quotient is the other factor, or x^2-1, which factors into (x+1)(x-1) by difference of squares.
\n" ); document.write( "Set those equal to zero, and the roots are -2,-1,and 1, on the interval {-4,4}. Those are all the values of a where f(a)=0.
\n" ); document.write( " $\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E3%2B2x%5E2-x-2%29\"$ \n" ); document.write( "

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