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Factoring of polynomials


In general case factoring of a polynomial is not always possible. But there are some cases, when it can be executed.

  1.  If all terms of a polynomial contain as a factor the same expression, it is possible to take it out of  brackets (see above).

  2. Sometimes grouping terms of a polynomial into brackets, one can find a common expression inside the  brackets, the expression may be taken out of the brackets as a common factor, and after this the same expression will be inside all brackets Then this expression must also be taken out of the brackets and the polynomial will be factored. 

E x a m p l e :    ax + bx + ay+ by = ( ax+ bx ) + ( ay + by ) =

                           = x ( a + b ) +  y ( a +  b ) = ( x + y ) ( a +  b ) .

  3. Sometimes including of new, mutually cancelled terms, helps to factor a polynomial.

E x a m p l e :   y 2 b 2  = y 2 + yb yb b 2 = ( y 2 + yb ) ( yb + b 2 ) =

                                           = y ( y + b ) b ( y + b ) = ( y + b ) ( y b ) .

  4. Usage of the formulas of abridged multiplication.

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