Steps to Factor Trinomials

In the previous post we have discussed about Polynomial Long Division and In today's session we are going to discuss about Steps to Factor Trinomials and How To Factor Trinomials Step By Step,
1. Firstly we are going to compare the given trinomial with the standard form of the trinomial i.e. ax>2 + bx + c and recognize the values of a, b, and c.
2. Now we are going to first look for the factor which is common in all the three terms. Once the common factor is recognized, we will bring it out of the three terms.
3. In the next step, we will split the middle term in such a way that the product of the two splitted terms will be equal to the product of the first and the third term and the sum will be equal to the middle term.
4. Further we will take out the common terms and make the factors.
Let us take the following trinomial :
18x>2 + 48*x*y + 32y>2
Here we will first take out the factor 2, from all the three terms and we get :
= 2 * (9x>2 + 24 * x * y + 16y>2)
= 2 * (3x)>2 + 2 * 3 * 4 * x * y + (4y )>2
= 2 * 3x + 4y>2
Thus we come to the observation that the step by step procedure must be followed in order to get the factorization of the trinomial.
If we are able to recognize the factors directly, relating it to some of the identity, then it becomes more easy for us to factorize. In case the trinomial is
4x>2 + 12x + 9
= (2x)>2 + 2 * 2 * 3x + 3>2
= (2x + 3 )>2
= (2x + 3 ) *(2x + 3 )
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