Rules for Factoring Trinomials

Trinomial is nothing but if we are having the function with three terms we can say that is a trinomial. Here we are going to learn what the rules available in factoring the trianomial are. There are three rules available for factoring trinomials. We will see the rules for factoring the trinomials with appropriate examples. Factoring the trinomial is depends on the degree of polynomials.

Rules for Factoring Trinomials:

If we want to factor a trinomial we have to start from the highest exponents. For factoring the trinomial first we have to find the greatest common factor and we have to simplify.

Example:

Factor the following trinomial 6x8 + 30 x7 + 36 x6

Solution:

First we have to find the factors of the greatest value

6x8 = 2. 3.  x2. x6

30x7 = 2. 3. 5.  x. x6

36 x6 = 2. 3. 6. x6

And here GCF of the variables 6x8, 30 x7, 36 x6 is 6x6

So the factor value is 6x6 (x2 + 5x + 6) = 6x6 (x + 2) (x + 3)

Rule 2 for factoring trinomial:

In rule 2 we have to see the factoring rules in algebra based on grouping the value. Here we are going to group the given trinomial and we have to factor this.

Example:

Factor the trinomial 3y2 + y – 4

Solution:

3y2 + y – 4

This is 3y2 + 4y – 3y - 4

So we get 3y(y + 4) - (3y + 4)

From this y (3y - 1) (3y + 4)

My forthcoming post is on Triangular Prism Net and Formula for Volume of a Rectangular Prism will give you more understanding about Algebra.

Other Rules for Factoring Trinomial:

Rule 3 for factoring trinomial:

If the given trinomial expression starts with the co – efficient of x2 we have to start from multiplication.

Example:

Factor the trinomial 10x2 - 14x + 4

Solution:

Given expression is 10x2 - 14x + 4

First we have to multiply 10 and 4

We get x2 - 13x + 40

Now if we divide this 10x2 - 4x – 10x + 4

x(10x –4) – (10x – 4)

(10x – 4) (x – 1)

These rules are helping us to factor the trinomial easily.