Factoring of polynomials
In general case factoring of a polynomial is not always possible. But there are some cases, when it can be executed.
If all terms of a polynomial contain as a factor the same expression, it is possible to take
it out of brackets (see above).
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 ) .
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 ) .
Usage of the formulas of abridged multiplication.