document.write( "Question 976987: Please help me solve this.
\n" ); document.write( "Find all zeros of the function and write the polynomial as a product of linear factors.\r
\n" ); document.write( "\n" ); document.write( "f(x)=3x^4+4x^3+13x^2+16x+4 \n" ); document.write( "

Algebra.Com's Answer #598481 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"f%28x%29=3x%5E4%2B4x%5E3%2B13x%5E2%2B16x%2B4\"$ .........write $\"13x%5E2\"$ as $\"x%5E2%2B12x%5E2\"$
\n" ); document.write( " $\"f%28x%29=3x%5E4%2B4x%5E3%2Bx%5E2%2B12x%5E2%2B16x%2B4\"$ ...........group
\n" ); document.write( " $\"f%28x%29=%283x%5E4%2B12%29%2B%284x%5E3%2B16x%29%2B%28x%5E2%2B4%29\"$
\n" ); document.write( " $\"f%28x%29=3x%5E2%28x%5E2%2B4%29%2B4x%28x%5E2%2B4%29%2B%28x%5E2%2B4%29\"$
\n" ); document.write( " $\"f%28x%29=%283x%5E2%2B4x%2B1%29+%28x%5E2%2B4%29+\"$
\n" ); document.write( " $\"f%28x%29=%283x%5E2%2Bx%2B3x%2B1%29+%28x%5E2%2B4%29+\"$
\n" ); document.write( " $\"f%28x%29=%28%283x%5E2%2Bx%29%2B%283x%2B1%29%29+%28x%5E2%2B4%29+\"$
\n" ); document.write( " $\"+f%28x%29=%28x%2B1%29+%283x%2B1%29+%28x%5E2%2B4%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "zeros:
\n" ); document.write( " $\"+0=%28x%2B1%29+%283x%2B1%29+%28x%5E2%2B4%29+\"$
\n" ); document.write( " $\"+0=%28x%2B1%29++\"$ => $\"x=-1\"$
\n" ); document.write( " $\"+0=+%283x%2B1%29+\"$ => $\"3x=-1\"$ => $\"x=-1%2F3\"$
\n" ); document.write( "and, since $\"%28x%5E2%2B4%29=0\"$ => $\"x%5E2=-4\"$ => $\"x=sqrt%28-4%29\"$ =>and zeros are $\"x=2i\"$ or $\"x=-2i\"$ ,\r
\n" ); document.write( "\n" ); document.write( "then $\"%28x%5E2%2B4%29=%28x-2i%29%28x%2B2i%29\"$ \r
\n" ); document.write( "\n" ); document.write( "and our the polynomial as a product of linear factors is:\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x%2B1%29+%283x%2B1%29%28x-2i%29%28x%2B2i%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );