Factorization of expressions, Mathematics

Above we have seen that (2x2 - x + 3) and (3x3 + x2 - 2x - 5) are the factors of 6x5 - x4 + 4x3 - 5x2 - x - 15. In this case we are able to find one factor given the other one. How are we going to solve in case when we are not given either of them. Finding the factors of a given expression forms the part of our attention now. First, we look at binomial expressions and once we understand this we move on to trinomials and polynomials. If the given expression is in the form of an identity (we look at them shortly) our job becomes easier otherwise we have to adopt trial and error method until we get at least one of the factors. Once we know one of the factors then by employing the division method we can get other factors.


Factorize x2 + 6x + 9.

If we substitute x = 1, the value of the expression will be (1)2 + 6(1) + 9 = 16

Since the value of the numerical expression is not 0, we substitute another value. We will continue to do so until we get a zero. 

If we substitute x = -1, the value of the expression will be (-1)2 + 6(-1) + 9 = 4

If we substitute x = 2, the value of the expression will be (2)2 + 6(2) + 9 = 25

If we substitute x = -2, the value of the expression will be (-2)2 + 6(-2) + 9 = 1

If we substitute x = 3, the value of the expression will be (3)2 + 6(3) + 9 = 36

We substitute x = -3, the value of the expression  will be (-3)2 + 6(-3) + 9 = 0

For x = -3, the value of the expression is 0. That is, x + 3 is one of the factors of the expression x2 + 6x + 9. To obtain the other factor we divide the expression by the factor we obtained. That will be

x + 3 )

x2 + 6x + 9

( x + 3


x2 + 3x



    3x + 9




(-)   3x + 9






From the division, we observe that x + 3 is the other factor. When this is equated to zero we obtain x = - 3. Therefore, the factors of x2 + 6x + 9 are (x + 3)(x + 3) or (x + 3)2.

In the above example we note that x2 + 6x + 9 = (x + 3)2.  Isn't this identical to a2  + 2ab + b2 = (a + b)2? The value of 'a' being x and that of 'b' equal to 3. This is one of the basic identities we get to see in algebra. 

Posted Date: 9/13/2012 3:16:53 AM | Location : United States

Related Discussions:- Factorization of expressions, Assignment Help, Ask Question on Factorization of expressions, Get Answer, Expert's Help, Factorization of expressions Discussions

Write discussion on Factorization of expressions
Your posts are moderated
Related Questions
Q. Define Number Line? Ans. A number line is a nice way to visualize and examine the ordering of the positive and negative numbers. Every positive and negative number that

Financial institutions often create synthetic instruments out of existing instruments.  In this case an investment bank plans to buy Treasury Bonds with 20-year maturities at their


The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(

How to Simplifying Square Roots ? To simplify square roots, 1. Factor the radicand into primes. 2. Circle each pair of like numbers. 3. For each pair of like numbers, place

find any integer from 1-128 on a logarithmic scale

Ray cut 6 pieces of rope . Each piece was between 67 and 84 inches long. What would be the total length of the 6 pieces of rope?


If r,R denote position vectors of points on the straight lines in the direction of a and b respectively, and if n is a unit vector perpendicular to both these directions, show that