document.write( "Question 962342: For the polynomial below, -1 is a zero.
\n" ); document.write( "F(x)= x^3+7x^2+24x+18
\n" ); document.write( "Express f(x) as a product of linear factors \r
\n" ); document.write( "\n" ); document.write( "f(x)= \n" ); document.write( "

Algebra.Com's Answer #587951 by MathLover1(20849) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "For the polynomial below, $\"-1\"$ is a zero.\r
\n" ); document.write( "\n" ); document.write( " $\"F%28x%29=+x%5E3%2B7x%5E2%2B24x%2B18+\"$ \r
\n" ); document.write( "\n" ); document.write( "Express $\"f%28x%29\"$ as a product of linear factors
\n" ); document.write( "since given the polynomial of degree $\"3\"$ , there will be three zeros and we can write it as:\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E3%2B7x%5E2%2B24x%2B18+=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29\"$ \r
\n" ); document.write( "\n" ); document.write( "since given $\"-1\"$ is a zero, we have $\"%28x-x%5B1%5D%29=%28x-%28-1%29%29=%28x%2B1%29\"$ as one linear factor\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E3%2B7x%5E2%2B24x%2B18+=%28x%2B1%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29\"$ ....to find other two linear factors, use long division and divide $\"%28x%5E3%2B7x%5E2%2B24x%2B18%29\"$ by $\"%28x%2B1%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E3%2B7x%5E2%2B24x%2B18%29%2F%28x%2B1%29=%28x-x%5B2%5D%29%28x-x%5B3%5D%29\"$ \r
\n" ); document.write( "\n" ); document.write( "-------( $\"x%5E2%2B6x%2B18\"$
\n" ); document.write( " $\"%28x%2B1%29\"$ |( $\"x%5E3%2B7x%5E2%2B24x%2B18\"$ )
\n" ); document.write( ".......... $\"x%5E3%2Bx%5E2\"$ .....................subtract
\n" ); document.write( "................. $\"6x%5E2%2B24x\"$
\n" ); document.write( "................. $\"6x%5E2%2B6x\"$ .....................subtract
\n" ); document.write( "........................... $\"18x%2B18\"$
\n" ); document.write( "........................... $\"18x%2B18\"$ .....................subtract
\n" ); document.write( "..................................... $\"0\"$ \r
\n" ); document.write( "\n" ); document.write( "so, we have\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B6x%2B18=%28x-x%5B2%5D%29%28x-x%5B3%5D%29\"$ ......now factor completely left side\r
\n" ); document.write( "\n" ); document.write( "first complete square $\"x%5E2%2B6x%2B18=%28x%2B3%29%5E2%2B9\"$ \r
\n" ); document.write( "\n" ); document.write( "so, solve for $\"x\"$ :\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%2B3%29%5E2%2B9=0\"$ if $\"%28x%2B3%29%5E2=-9\"$ => $\"x%2B3=sqrt%28-9%29\"$ => $\"x%2B3\"$ =ą $\"3i\"$ \r
\n" ); document.write( "\n" ); document.write( "=>solutions $\"x%5B2%5D=-3%2B3i\"$ and $\"x%5B3%5D=-3-3i\"$ \r
\n" ); document.write( "\n" ); document.write( "then, your polynomial is:\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E3%2B7x%5E2%2B24x%2B18+=%28x%2B1%29%28x-%28-3%2B3i%29%29%28x-%28-3-3i%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E3%2B7x%5E2%2B24x%2B18+=%28x%2B1%29%28x%2B3-3i%29%28x%2B3%2B3i%29\"$ \r
\n" ); document.write( "\n" ); document.write( "or\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=%28x%2B1%29%28x%2B3-3i%29%28x%2B3%2B3i%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );