Trinomial Factoring Program

Introduction to trinomial factoring program:-
An algebraic expression containing three terms is called a trinomial.for example 2x+3y + 4z is a trinomial.
When we multiply two binomials, we get a trinomial. For ex (2x+5)(x+4) = 2x2 + 13x + 20 which is a trinomial.
So it follows that  we can find the factors of a trinomial.
Let us see some formulas that we use for trinomial factoring program.I like to share this What is a Trinomial with you all through my article.

Formulas Used in Trinomial Factoring Program:-

There are certain formulas that assist us when we need to factorise the trinomials.v
1. a2 + 2ab + b2  = (a + b)2
Let us do a problem bases on this formula.
# Factorize 25x2 + 30xy + 9y2
Using the above formula we find a2 = 25x2 => a = 5x;  2ab = 30xy = 2*5*3*x*y ; b2 = 9y2 = > b = 3y
Hence the solution is (a+b)2  =  (5x+3y)2= (5x+3y)(5x+3y)
Solution: The factors of 25x2+ 30xy + 9y2 = (5x+3y)(5x+3y)
2. Here is another formula to assist us to do the trinomial factoring program.
It is a2 - 2ab + b2 = (a - b)2
# Factorize 16x2 - 24xy + 9y2
This problem confirms to the second formula given here
Hence if a2 = 16x2 then a = 4x; b2 = 9y2 => b= 3y and  -2ab = -24xy => 2*4*3*x*y
Hence the factors of 16x2 - 24xy + 9y2  = (4x - 3y)2  = (4x-3y)(4x -3y)
Solution: The factors of 16x2 - 24xy + 9y2 = (4x - 3y)(4x - 3y)
Here is another formula to help trinomial factoring program
3. a2 + (a+b)x + ab =  (x+a)(x+b)
The second term is addition of two factors and the third term is the multiplication of two terms.
Hence our steps would be (1) to find the factors of a and b (2) select the factors that satisfy a+b
# Factorise x2 + 12x + 35
Solution:-
Here a+b= 12 and ab = 35
Step 1 : Let us find the factors of ab that is 35
Factors of 35 are (1,35), (5,7)
Step 2 : Let us add the factors and see which satisfies (a+b)
If we add 1+35 = 36 which is not what we want.
If we add 5+7= 12 which is what we want.
So the factors are (x+5)(x+7)
Hence  x2 + 12x + 35  can be factored as (x+5)(x+7)
Solution of the problem is (x+5)(x+7).

Probles Based on Trinomial Factoring Program:

Let us do one more problem based on the third formula .
# Factorize x2 +6x - 27
Solution:-
In this problem (a+b) = 6 and ab = -27
Step 1 find the factors of 27
(1,27), (3,9)
Let us add them 1+27=28 which is not the 2nd term 6 So we discard it.
Let us add 3+9 = 12 which is again not +6
But the third term has a negative sign.
So let us do 9-3 = +6
Now our formula changes slightly.  we need to put a negative number also
Hence we write it as (x+9)(x-3) and note that 9-3=6 which is the middle term and 9*-3 = -27 which is the last term             Hence the solution is x2 + 6x - 27 = (x+9)(x-3)
Answer : (x+9)(x-3)
Thus trinomial factoring program can be made easy if we learn the formulas that assit the factoring.