document.write( "Question 1060004: Factorize the polynomial $\"+f%28x%29+=+x%5E3+-+7x+%2B+6+\"$ completely .Thank-you ! \n" ); document.write( "

Algebra.Com's Answer #675049 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( " $\"f%28x%29\"$ = $\"x%5E3+-+7x+%2B+6+\"$ = (x-1)*(x-2)*(x+3).\r
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\n" ); document.write( "\n" ); document.write( "Hint: You can easily check that 1 is the root of the polynomial $\"x%5E3+-+7x+%2B+6+\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Then divide the given polynomial by (x-1) (long division) without a remainder, according to the \"Remainder Theorem\".\r
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\n" ); document.write( "\n" ); document.write( "Then analyse the obtained quadratic quotient.
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\n" ); document.write( "\n" ); document.write( "From Wikipedia (https://en.wikipedia.org/wiki/Polynomial_remainder_theorem): \r
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document.write( "     The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by a linear polynomial  x-a is equal to  f(a).      \r\n" );
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document.write( "     In particular,  x-a is a divisor of  f(x) if and only if f(a)=0.\r\n" );
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