Hello students, in this topic we are going to learn about Factoring Trinomials. First we have to understand the term trinomial. A trinomial is basically an equation which is present in form of x2 + bx + c, these are types of equations you read in algebra. So first we have to understand the meaning of the factorization. It means that if we have any value then break that value in their elementary numbers we can understand it by an example as 35 is factor in its smallest terms as ( 7 * 5 ) which means “ 7 times of 5 is 35 “ . (To get help on icse click here)
Now factoring trinomials can be understand by an example as a2 + 14 a + 24 than we factor the terms of the equation in form that it's factor have the multiplication 24 and their addition will be 14a. So we write the factor of the 24 as ( 2 * 2 * 2 * 3 ) then we arrange these factors as their total is equal to 14 , so we do the splitting as (a + 2 ) ( a + 12 ) So after factor trinomials solver we get the equation as
=a2 + 12 a + 2a + 24 = a ( a + 12 ) +2 (a + 12 )
= ( a + 12 ) (a + 2 )
The factor of trinomial is a2 + 14 a + 24 are ( a + 2 ) and ( a + 12 ).
Now we will take another example for factoring the trinomial as an equation
p2 + 7p -30
Here the sign of the third term is negative so the factors of it will be in form if ( p + k)( p - k)
So the factor of -30 which have the difference 7 is as follows:-
30 = ( 2 * 3 * 5 * 1 ) so we make the pair as it have the difference 7 so it is 10 - 3
And we write it as p2 + 10p -3p -30 = p ( p + 10 ) -3 ( p + 10 )
= ( p – 3 ) ( p + 10 )
So the factor of equation p2 +7p – 30 is ( p -3 ) ( p + 10 ).
In the next topic we are going to discuss Multiplying Trinomials and In the next session we will discuss about Multiplying Trinomials.