document.write( "Question 327180: find the zeros of the following polynomial f(x)= x^3-4x^2-7x+10 \n" ); document.write( "

Algebra.Com's Answer #234383 by galactus(183) $\"\"$ $\"About$

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Per the Rational Root Theorem, we see that 1, 2, 5 are possible roots.\r
\n" ); document.write( "\n" ); document.write( "We know this by looking at the constant term, 10. What divisors does 10 have?.\r
\n" ); document.write( "\n" ); document.write( "1,2,5,10. We can also check the negative of these as well. \r
\n" ); document.write( "\n" ); document.write( "By using division, we can test these roots and see. Try 5. If we divide the given cubic by x-5 and it reduces to a quadratic, we have a root.\r
\n" ); document.write( "\n" ); document.write( "Doing so, reults in x^2+x-2\r
\n" ); document.write( "\n" ); document.write( "Yep, 5 is a root.\r
\n" ); document.write( "\n" ); document.write( "Now, a little ol' quadratic that is easily factorable.\r
\n" ); document.write( "\n" ); document.write( "What two numbers when multiplied equal -2 and when added equal 1?.\r
\n" ); document.write( "\n" ); document.write( "How about 2 and -1?.\r
\n" ); document.write( "\n" ); document.write( "x^2+2x-x-2\r
\n" ); document.write( "\n" ); document.write( "x(x+2)-(x+2)\r
\n" ); document.write( "\n" ); document.write( "(x-1)(x+2)\r
\n" ); document.write( "\n" ); document.write( "So, the factored form of the cubic is (x-5)(x-1)(x+2)\r
\n" ); document.write( "\n" ); document.write( "So, it has roots 5,1,-2.\r
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