document.write( "Question 675207: Show that the given values of c are zeros of P(x), and find all other zeros of P(X) \r
\n" ); document.write( "\n" ); document.write( "P(X)= 3x^4-x^3-21x^2-11x+6 c=(1/3), -2 \n" ); document.write( "

Algebra.Com's Answer #419731 by ReadingBoosters(3246) $\"\"$ $\"About$

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0 = $\"3x%5E4-x%5E3-21x%5E2-11x%2B6\"$
\n" ); document.write( "...
\n" ); document.write( "c = 1/3
\n" ); document.write( "3c = 1
\n" ); document.write( "3c - 1 = 0
\n" ); document.write( "(3x-1)
\n" ); document.write( "...
\n" ); document.write( "c = -2
\n" ); document.write( "c + 2 = 0
\n" ); document.write( "(x+2)
\n" ); document.write( "...
\n" ); document.write( "(3x-1)(x+2)
\n" ); document.write( " $\"3x%5E2+%2B+6x+-+x+-+2\"$
\n" ); document.write( "From the given zeros we know
\n" ); document.write( " $\"3x%5E2+%2B+5x+-+2\"$
\n" ); document.write( "...
\n" ); document.write( "To find the remaining factors, divide
\n" ); document.write( " $\"%283x%5E4+-+x%5E3+-+21x%5E2+-+11x+%2B+6%29%2F%283x%5E2%2B5x-2%29\"$
\n" ); document.write( "...
\n" ); document.write( " $\"3x%5E2+%2B+5x+-+2\"$ goes into $\"3x%5E4+-+x%5E3+-+21x%5E2+-+11x+%2B+6\"$ : x^2
\n" ); document.write( "to get
\n" ); document.write( " $\"3x%5E4+%2B+5x%5E3+-+2x%5E2\"$
\n" ); document.write( "subtracting
\n" ); document.write( " $\"3x%5E4+-+3x%5E4+-+x%5E3+-+5x%5E3+-+21x%5E2+-+-2x%5E2\"$
\n" ); document.write( "yielding
\n" ); document.write( " $\"-6x%5E3+-+19x%5E2\"$
\n" ); document.write( "...
\n" ); document.write( " $\"3x%5E2%2B5x-2\"$ goes into $\"-6x%5E3-19x%5E2-11x\"$ : -2x
\n" ); document.write( "to get
\n" ); document.write( " $\"-6x%5E3+-+10x%5E2+%2B+4x\"$
\n" ); document.write( "subtracting
\n" ); document.write( " $\"-6x%5E3+-+-6x%5E3+-+19x%5E2+-+-10x%5E2+-+11x+-+4x\"$
\n" ); document.write( "yielding
\n" ); document.write( " $\"-9x%5E2-15x\"$
\n" ); document.write( "...
\n" ); document.write( " $\"3x%5E2%2B5x-2\"$ goes into $\"-9x%5E2-15x%2B6\"$ : -3
\n" ); document.write( "to get
\n" ); document.write( " $\"-9x%5E2+-+15x+%2B+6\"$
\n" ); document.write( "subtracting
\n" ); document.write( " $\"-9x%5E2+-+-9x%5E2+-+15x+-+-15x+%2B+6+-+6\"$
\n" ); document.write( "yielding
\n" ); document.write( "0
\n" ); document.write( "...
\n" ); document.write( "...
\n" ); document.write( " $\"%283x%5E4+-+x%5E3+-+21x%5E2+-+11x+%2B+6%29%2F%283x%5E2%2B5x-2%29+=+x%5E2-2x-3\"$
\n" ); document.write( "...
\n" ); document.write( " $\"x%5E2-2x-3\"$
\n" ); document.write( "(x-3)(x+1)
\n" ); document.write( "...
\n" ); document.write( "All for zeros
\n" ); document.write( " $\"1%2F3\"$ , - 2 : given
\n" ); document.write( "3, -1 : solved
\n" ); document.write( ".....................
\n" ); document.write( "Delighted to help.
\n" ); document.write( "-Reading Boosters
\n" ); document.write( "Website: www.MyHomeworkAnswers.com
\n" ); document.write( "Wanting for others what we want for ourselves. \n" ); document.write( "

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