We know that the trinomial is the polynomial formed by three terms. To learn about Factoring Trinomials, we say that the standard form of the trinomial is ax>2 + bx + c.
To find the factors of the above given polynomial , we say that we will either write it in form of some or the other identity or we will try to factorize it by the splitting method. In the splitting method, we say that the middle term of the trinomial is split in such a way that the sum of the two terms is equal to bx (i.e. the second term) and the product of the two split term is equal to the product of the first and the third term of the trinomial.
Let us look at the following examples:
If we have the polynomial: 4x>2 + 12x + 9
Here we can write the above given polynomial as ( 2x )>2 + 2 * 2x * 3 + 3>2
We observe that the above given polynomial is in the form of the identity (a + b) >2 = a>2 + 2 * a * b + b>2
So it can be written as (2x + 3) >2
If we solve the polynomial by splitting the second term we say it can be written as :
4x>2 + 6x + 6x + 9
= 2x * ( 2x + 3 ) + 3 * ( 2x + 3 )
= ( 2x + 3 ) * ( 2x + 3 ) = ( 2x + 3 ) >2 Ans
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