Methods of Factoring Trinomials

Introduction :

Trinomials:

In elementary algebra, a trinomial is a polynomial consisting of three terms or monomials.

Trinomial expressions:

1. 3x + 5y + 8z with x, y, z variables

2. 3t + 9s2 + 3y3 with t, s, y variables

3. 3ts + 9t + 5s with t, s variables

4. Axaybzc + Bt + Cs with x, y, z, t, s variables, a, b, c nonnegative integers and A, B, C any constants.

5. Pxa + Qxb + Rxc where x is variable and constants a,b,c are nonnegative integers and P, Q, R any constants.

6. x2 + 8x + 15 where x is variable ( source : wikipedia)

Methods of Factoring Trinomials:

By using the following two methods we can factoring the trinomials.

Factoring trinomials Method 1:

The co-efficient of the first term (that is x2) is one. That is a=1.

x2+bx+c=(x-r1)(x-r2), Here r1 and  r2 are the roots of the trinomials.

We can say, (x - r1), (x - r2) are the factors of the trinomial.

Example Problems on methods of factoring trinomials :

By go through the following problem you can learn the method 1 of factoring the trinomials.

Example 1:

Factor the trinomial x2- 10 x +16

Solution:

Given, x2- 10 x +16

We need to factoring the given trinomial,

16   (product)

/    \   

- 8      - 2

\    /

-10     (sum)

So we can write the given equation into,

x2- 10 x +16 = x2 - 2x - 8x +16

= x ( x-2 ) - 8( x-2 )

= ( x - 8 ) ( x - 2 )

Answer: (x-8) and (x-2) are the factors of the given trinomial.

Verification:

(x-8) (x-2)  = x (x - 8) -2 (x - 8)

= x2-8x -2x+16

(x-8) (x-2)  = x2 -10x + 16

Example 2

Find the factors of   x2+ 3x -18.

Solution:

Given, x2+ 3x -18

We need to factoring the given trinomial,

-18 ( Product)

/     \

6       - 3

\     /

3 ( sum)

So we can rewrite the given equation into,

x2+3x - 18 = x2-3 x+6x -18

= ( x2-3x ) + ( 6x-18 )

= x ( x-3 ) + 6 ( x -3 )

= (x - 3) (x + 6)

Answer: factors (x-3) and (x+6)

Algebra is widely used in day to day activities watch out for my forthcoming posts on how to write an algebraic expression and example of algebraic expression. I am sure they will be helpful.

Methods of Factoring Trinomials:

Factoring trinomials Method 2:

The co-efficient of the first element( x2) trinomial is greater than one. That is a > 1.

The following example will help you to understand this method.

Example:

Factoring the trinomial 6x2- 3x - 3.

Solution:

Given, 6x2- 3x - 3 

To factor the trinomial, multiply the coefficient of first term with the constant i.e. 6 * (-3)=-18

- 18    (product)

/    \

- 6     3

\     /

- 3    (sum)

6x2- 3x - 3  =  6x2- 6x + 3x -3

=  6x (x - 1) + 3(x-1)

= (6x+3) (x-1)

= 3(2x+1)(x-1)

Answer: Factors of the given trinomial 3, (2x+1), (x-1)