document.write( "Question 737612: Solve. Remember to use the Rational Zero Theorem, Descartes' Rule of Signs, reduce to a quadratic, and then solve by using factoring or the Quadratic Formula.\r
\n" ); document.write( "\n" ); document.write( "f(x) = x4 + 6x3 + 7x2 - 6x - 8 \n" ); document.write( "
Algebra.Com's Answer #450473 by josgarithmetic(39617)\"\" \"About 
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One change in sign so expect one positive root, according to Descartes Rule of Signs. \r
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\n" ); document.write( "\n" ); document.write( "(-x)^4+6(-x)^3+7(-x)^2-6(-x)-8
\n" ); document.write( "x^4-6x^3+7x^2+6x-8
\n" ); document.write( "That is three changes in sign, so expect three negative roots according to Rule of Signs.\r
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\n" ); document.write( "\n" ); document.write( "Possible roots to check using Rational Roots Theorem and synthetic division would be -1, -2, -4, -8, 1, 2, 4, 8.\r
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\n" ); document.write( "\n" ); document.write( "Best to check for the negative roots first because we expect MORE of them.\r
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\n" ); document.write( "\n" ); document.write( "I will omit showing the actual synthetic divisions, but here is what I checked and what found:
\n" ); document.write( "Check -2: Yes, root. Zero remainder. Quotient \"x%5E3%2B4x%5E2-x-4\".
\n" ); document.write( "Check -4: Yes, root. Zero remainder. Quotient \"x%5E2-1+=+%28x-1%29%28x%2B1%29\".
\n" ); document.write( "And from that last quotient, we see that roots are +1 and -1.\r
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\n" ); document.write( "\n" ); document.write( "Summary of Roots found:
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\n" ); document.write( "-4, -2, -1, and +1
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