Factoring
To factor a polynomial means to find the factors (numbers that multiply)
which form the polynomial product. The first factor that you should
look for is the
Next, once you have factored the GCF
(if there is a GCF in the polynomial), consider the length of the
polynomial. If the polynomial has 1) _{}2) _{}3) _{}4) _{}If the trinomial is complicated by having a
coefficient in front of the squared variable term, then you may want to
try the method of factoring trinomials by "re"grouping.
In this method, a trinomial is transformed into a four-termed polynomial and
then factored by grouping as described above. _{}, you can substitute. This would now look
like: _{}Now, take _{} and factor by grouping as described above and the
result would be _{}If the polynomial has _{} and the square root of 25 = 5, now insert as follows: _{} Notice, the result is a pair of conjugates
which means two factors that look alike except
that one has a + and one has a connecting the terms of the binomials.
Note: you cannot factor the sum of squares.To factor the sum or difference of cubes, you must
know that the result is a binomial factor and a trinomial factor.
Also, you must memorize the sign pattern. The pattern is easily
memorized by using the mnemonic O stands for
(the second sign is the
opposite of the binomial being factored), and Opposite
AP stands for
(the last sign is always positive.)Always PositiveTo factor _{}, which is the difference of cubes, first write down the
sign pattern
( __ __ )( __ + __ + __ ). Find the cube roots of both of the terms of the polynomial. The cube root of _{} and the cube root of 27 = 3. Next, fill in the blanks by
placing 2x in the first blank and 3 in the second blank. Square 2x to get
_{} for the third blank, multiply (2x)(3) to get 6x for the
fourth blank and square 3 to get 9 for the last blank. The result would
look like this: _{}. The sum of cubes, _{
} , would be the same as above, except for the signs, (
__ + __ )( __ __ + __ ).
Since and
,
then_{ }The last step in factoring a
polynomial is considering the question, Practice is the key to any of these factoring methods! The views and
opinions expressed in this page are strictly those of Mary Lou Baker. This page was edited on 19-Sep-2007 |