document.write( "Question 1172954: For the standard form polynomial f(x)=2x^4-13x^3+2x^2+82x-40 find its roots and write it as the product of linear factors.
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Algebra.Com's Answer #798137 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "(previous response replaced -- contained arithmetic errors....)

\n" ); document.write( "By the rational roots theorem, the possible rational roots are

\n" ); document.write( "(plus or minus) {1, 2, 4, 5, 8, 10, 20, 40; 1/2, 5/2}

\n" ); document.write( "You can test each rational root using synthetic division; but that is very tedious.

\n" ); document.write( "Finding the roots using a graphing calculator is fast and easy. The factorization is

\n" ); document.write( " $\"%28x-4%29%282x-1%29%28x%5E2-2x-10%29\"$

\n" ); document.write( "The quadratic formula gives the roots of the quadratic factor as

\n" ); document.write( " $\"1%2Bsqrt%2811%29\"$ and $\"1-sqrt%2811%29\"$

\n" ); document.write( "So if you really need to write the polynomial as a product of linear factors, it is

\n" ); document.write( " $\"%28x-4%29%282x-1%29%28x-%281%2Bsqrt%2811%29%29%29%28x-%281-sqrt%2811%29%29%29\"$
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