document.write( "Question 695069: Find all real and complex zeros of P(x)=x^3-x^2-4x-6. Show all work. \n" ); document.write( "

Algebra.Com's Answer #428322 by KMST(5328) $\"\"$ $\"About$

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Rational zeros of P(x) must be factors of 6 (with + or - signs.
\n" ); document.write( "Choices are: -6, -3, -2, -1, 1, 2, 3, and 6.
\n" ); document.write( "P(3)= $\"3%5E3-3%5E2-4%2A3-6=27-9-12-6=0\"$ so $\"x=3\"$ is a zero.
\n" ); document.write( "That means that $\"%28x-3%29\"$ is a factor of P(x).
\n" ); document.write( "Dividing, we find
\n" ); document.write( " $\"%28x%5E3-x%5E2-4x-6%29%2F%28x-3%29=x%5E2%2B2x%2B2\"$ <--> $\"x%5E3-x%5E2-4x-6=%28x-3%29%28x%5E2%2B2x%2B2%29\"$
\n" ); document.write( "p(x)= $\"%28x-3%29%28x%5E2%2B2x%2B2%29\"$
\n" ); document.write( "Besides, $\"highlight%28x=3%29\"$ , the zeros of P(x) are the solutions to $\"x%5E2%2B2x%2B2=0\"$
\n" ); document.write( "That is easy to solve by \"completing the square\", but feel free to use the quadratic formula, if you like it better.
\n" ); document.write( " $\"x%5E2%2B2x%2B2=0\"$ --> $\"x%5E2%2B2x%2B1=-1\"$ --> $\"%28x%2B1%29%5E2=-1\"$ --> $\"highlight%28x=-1+%2B-+i%29\"$ \n" ); document.write( "

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