Trinomials

Previously we have discussed about how to do trigonometric functions and now we are starting a new topic that is Trinomials which comes under maharashtra board,It is basically a part of polynomial .as you know tri means three so trinomial means an expression(algebraic expression,rational expressions) that contains three terms. It has a wide application in quadratic functions. 2X+3Y+2 is also a trinomial because it contain three terms 2X,3Y and 2. So by this example we can create a general form i.e.-AX+BY+C. This equation is known as trinomial equation.
Now let’s do some more operation on trinomial before going for multiplying trinomial. Trinomials can be factorized which we will see by an example.
X²+5X+4 is a trinomial and we need to factorize them so what we need to do is we need to factorize the middle term with respect to last term. Here the middle term is 5 and last term is 4 so we can factorize 5 with respect to 4 as 5-1=4 and 4*1=4 so we just need to write the above example as
X²+4X-X+4
We just divided the equation in 2 parts and then just taken X common from 1^st part and -1 from second part
X(X+4)-1(X+4)
X+4 is common in both the parts so we take that as well common
(X+4) (X-1)
These are the required factors.
Now we will see how to multiply trinomials(want to Learn more about Trinomials ,click here),
Example: multiply (x² +4x+5) with (x² +3x +6 )
We can multiply both the trinomials, but for that we need to remember following points given below:
We have to multiply the first member with all the members of second trinomial and same thing have to be done with the other variable, and we also need to remember that powers are added up in multiplication.

(x² +4x+5)* (x² +3x +6)
=x²(x² +3x +6) +4x(x² +3x +6)+5(x² +3x +6)
=x⁴+3x³+6x² +4x³+12x²+24x+5x²+15x+30
Now we will arrange them according to their power in descending order.
=x⁴+7x³+23x²+39x+30
This is the required result
Note: in multiplying Trinomials, order is not important,if we multiply (x² +4x+5) with(x² +3x +6 ) or (x² +3x +6 ) with(x² +4x+5) both will give the same result.
Now I think you well understood about the trinomial and Multiplying Trinomials, you just need to practice more all questions are about practicing so just practice hard. This is a brief introduction about trinomials in the next article we will learn about Binomial Distribution by splitting the middle term.