document.write( "Question 892677: Find two different polynomials j(x) and g(x) such that the degree of each polynomial is greater than 1 and j(5) = g(5) = 0. I don't even know where to start. \n" ); document.write( "

Algebra.Com's Answer #540699 by josgarithmetic(39620) $\"\"$ $\"About$

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This allows many possible polynomials j and g.\r
\n" ); document.write( "\n" ); document.write( "Needing a root to be 5, each function would have a binomial factor x-5. Generally, you can have both j and g in degree 2, which is greater than degree 1.\r
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\n" ); document.write( "\n" ); document.write( " $\"g%28x%29=%28x-m%29%28x-5%29\"$ and $\"j%28x%29=%28x-p%29%28x-5%29\"$ and that m, and p, are any real numbers. You can also include a factor for each polynomial, also of real numbers.\r
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\n" ); document.write( "\n" ); document.write( "If k and h are both any real numbers NOT equal to zero, then you can have
\n" ); document.write( " $\"g%28x%29=k%28x-m%29%28x-5%29\"$ and $\"j%28x%29=h%28x-p%29%28x-5%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "The problem specified that each degree must be greater than 1; and my general example used degree 2 for both functions. You can choose higher degrees if desired. You can choose something like $\"j%28x%29=%28kx%5E2-bx%2Bc%29%28x-5%29\"$ for real numbers k, b, c, and recognize that j(x) is in degree 3. This still has a root of 5. \n" ); document.write( "

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