document.write( "Question 731401: f(x)= 2x^3+9x^2+14x+5\r
\n" ); document.write( "\n" ); document.write( "I am supposed to find the actual zeros( I have only come up with -1/2 )
\n" ); document.write( "and I am supposed to reduce/ show linear factors? \n" ); document.write( "

Algebra.Com's Answer #447106 by josgarithmetic(39618) $\"\"$ $\"About$

You can put this solution on YOUR website!
You basically just have to do the work. Your roots to check would be based on Rational Roots Theorem and your root's numerator would be any of 1, or -1, or 5, or -5. The denominator would be any of 1 or -1 or 2 or -2. No more than sixteen roots to check for. Synthetic division will help make the work go fast. Each root you find makes the rest of the task easier/faster.\r
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\n" ); document.write( "\n" ); document.write( "SINCE YOU FOUND A CORRECT ROOT of -1/2, you must have found the quotient to be $\"2x%5E2%2B8x%2B10\"$ , which is the same as $\"2%28x%5E2%2B4x%2B5%29\"$ . [yes, I checked -1/2 as a root to be sure.] The resulting quadratic is not factorable, so use general solution to quadratic equation (no real need to continue with synthetic division and checking roots that way).
\n" ); document.write( "The roots of the quadratic factor are $\"-2-i\"$ and $\"-2%2Bi\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Summary:
\n" ); document.write( "The function factors to $\"f%28x%29=2%28x%2B1%2F2%29%28x%5E2%2B4x%2B5%29\"$ , and the roots are $\"-1%2F2\"$ , $\"-2-i\"$ , and $\"-2%2Bi\"$ . \n" ); document.write( "

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