Factoring Trinomials

Let’s work on the polynomials and learn to factorize them, but before getting into the factorization of trinomials let’s understand what trinomials are?  And the answer will come out of your mind only.

Just read the word “trinomial” carefully and there the answer is. Did you get it? The name trio + nomials’ literally mean the trio of polynomials. And finding the product of two polynomials is exactly what factorization of polynomials’ mean.

Now, when you are clear with factoring trinomials let’s pay a look how trinomials look like.

Examples of trinomials:

3x²+2x+1

A trinomial always has three terms. Let’s discuss the term with above written equation

1st term is the squared one i.e. 3x²

2^nd term is a regular term i.e. 2x

And, the final 3^rd term is a number i.e. 1

Note: When an exponent is greater than 2 in a term that is not considered to be a trinomial.

Example: 5x³ + 6x² + 9

We can’t factorize it as a trinomial because the first term is having an exponent that is not below 2 and the second term is also not a regular term.

Now, it’s time to learn factorization:

To factor a trinomial in the form x² + bx + c

• Find two integers, m and n, whose product is c and whose sum is b.
• Rewrite the trinomial as x² + mx + nx + c and then use grouping and the distributive property to factor the polynomial.
• Once you have checked the greatest common factor and factored it out, then you can factor the trinomial.
• The resulting factors will be (x +m) and (x + n), the binomials.  
• Practical example of factorizing a polynomial is a s follows:

Example 1:

Problem: X² + 5x +6

Solution: (X+3) (X+2)

Detailed explanation of the solution is as follows:

X²+3x + 2x + 6:   We took two integers 3 and 2 whose product is the 3^rd term and when added produce the second term and we wrote it as x² + mx + nx + c.

X(x=3) 2(x+2):   then, we grouped the polynomial to factorize the equation.

(x+3) (x+2):     here, the factors are.

Now, it’s time to deal with quadratic equations:

Example 2:

Problem:   x² + x – 6

Solution:  x² +3x-2x-6

               X (x+3) – 2(x-2)

              (x+3) (X-2)

Example 3:

Problem:   x² – 7x + 6.

Solution: x² –6x – x + 6

              X (x-6) 1(x-6)

             (X-1)  (X-6)

So, this was one of the most interesting chapters called, factorizing trinomials.

Easy steps to follow skim your mind and pen down the solutions. Hope you enjoyed learning with us. Practice more and more and be wonderful with factoring trinomials.

Some useful links:

1. http://www.mathwarehouse.com/algebra/factor/how-to-factor-trinomials-step-by-step.php The above url can teach you the easy methods to factorize the things, also provide you practice sheets for the same.
2. http://www.mesacc.edu/~scotz47781/mat120/notes/factoring/trinomials/a_is_not_1/trinomials_practice.html You can visit the above link to practice the problems with explained solutions.
3. http://www.coolmath.com/algebra/04-factoring/05-trinomials-undoing-FOIL-2-01 Use the above link to study the easy methods of factoring trinomials.