document.write( "Question 425389: This is the last problem on my review and I spent 3 hours at math lab tonight and didn't get quite finished. If possible could you please explain this problem to me.\r
\n" ); document.write( "\n" ); document.write( "x^3 - 7x^2 - 14x + 48 = 0\r
\n" ); document.write( "\n" ); document.write( "I know the answers are x = -3, 2, 8\r
\n" ); document.write( "\n" ); document.write( "But I don't understand how to work it out. \r
\n" ); document.write( "\n" ); document.write( "Thanks very much! \r
\n" ); document.write( "\n" ); document.write( "Shelby \n" ); document.write( "

Algebra.Com's Answer #296223 by richard1234(7193) $\"\"$ $\"About$

You can put this solution on YOUR website!
There is a lot of brute-forcing involved in this problem. It is quite difficult to factor a cubic but you can use the rational root test to find a rational root and reduce it to a quadratic equation. There is also a cubic formula, but I doubt anyone can memorize it.\r
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\n" ); document.write( "\n" ); document.write( "For example, suppose you find x=2 using the rational root test. Then you can divide $\"%28x%5E3+-+7x%5E2+-+14x+%2B+48%29%2F%28x-2%29\"$ using either long or synthetic division. You will obtain a quadratic equation with no remainder, then find that the roots of that equation are -3 and 8. \n" ); document.write( "

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