Trinomials
In algebra, a trinomial is a type of polynomial in which there are only three terms or three monomials.
For Example – 3 x + 5 y + 8 z is a Trinomials with variables x, y and z.
3 t s + 8 t + 3 s is a trinomial with variables t and s.
3 x 2 + 4 x + 5 is a trinomial with variable x, it is also called as a quadratic trinomial.
We can also write the definition of a trinomial with respect to its equation which says, a trinomial equation is an equation involving three terms, an example of trinomial equation is x = q + x m.
We have studied above about the quadratic trinomials, this type of trinomials are very important as they form a separate field in algebra known as Quadratic Expressions.
In general a quadratic trinomial is written as a x 2 + b x + c, where a cannot be equal to 0.
The trinomial is solved by factoring the expression,
for example if we take into consideration the quadratic trinomial, its factors could be found by using the factoring method.
The factors of our trinomials are written in a general form as (x + _) ( x + _ ).
For Example – Solve – x 2 + 5 x + 6.
Now in this question we have to find the possible factors of 6, so that they add up to give the sum 5. The factors of 6 could be 6 x 1 and 3 x 2.
so in this only 3 and 2 add upto give 5 so these could be our factors. So the middle term could be written as x2 + 3 x + 2 x + 6.
so now taking x common from the first two terms and 2 from the last two term we get
x ( x + 3 ) + 2 ( x + 3). now we can take (x+3) as our common term from the expression, so out values becomes, ( x + 3 ) ( x + 2 ).
now x= -3, -2
Let’s solve one more example for more understanding.
Solve – x 2 – 5 x + 6.
in this problem we can see that the coefficient of x is negative, so our sum should also be negative.
So we break 6 as (-3,-2) and (-6, +1).
so our factors would be -3 and -2.
So now our equation becomes ( x – 3 ) ( x – 2 ).
so our value for x = 3, 2.
For more information on Significant Figure and methods for Dividing Trinomials get connected to MathCaptian.com.
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