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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.

Example:

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.

Example:

y² – b² = y² + yb – yb – b² = ( y² + yb ) – ( yb + b² ) =
= y ( y + b ) – b ( y + b ) = ( y + b ) ( y – b ) .

4. Usage of the formulas of abridged multiplication.

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