What are simple trinomials and how to factor them?

 

What is a trinomial?

• A trinomial is an algebraic expression made up of 3 terms.

• For example, x^2+2x+4.

• This is a trinomial because it is made up of three terms which are, x^2, 2x, and 4.

 

A simple trinomial is in the form of ax^2+bx+c

However, the "a" value can only be 1. 

An example of a simple trinomial is x^2+7x+12

 

How do we factor this?

The factored form of a simple trinomial is in the form of (____) (____)

In order to learn how to factor, we must first learn how to expand.

 

Let's try an eaxmple...

Expand (x+2) (x+3)

We have to multiply the first bracket by the second one, and in order to do this, we must multiply each term in the first bracket, by each term in the second one.

• x multiplied by x equals to x^2.

• x multiplied by 3 equals to 3x.

• 2 multiplied by x equals to 2x.

• 2 multiplied by 3 equals to 6.

• So we have x^2+3x+2x+6.

• Now, collect like terms (3x and 2x are like terms).

• We get x^2+5x+6.

 

As you can see, the expression we get when we multiply is in the simple trinomial form. 

Now let's factor the same expression of x^2+5x+6.

• First start with (____) (____).

• Now, which two variables multiply together to get x^2.

• The answer is x multiplied by x.

• So we get (x__) (x__).

• The other two numbers need to be a factors of 6, and they need to multiply to 6, while they also need to add together to 5.

• The factors of 6 are 1,2,3,6.

• From theses, which two numbers add to 5.

• They are 2 and 3.

• So we get (x+2) (x+3). 

• 2 multiplied by 3 equals to 6, and 2+3 equals to 5!

 

Want to try another example?

Sure, let's factor x^2-9x+18

• First start with (___) (___).

• Which two variables multiply together in order to get x^2.

• They are x multiplied by x!

• We get (x__) (x__).

• The other two numbers need to be a factors of 18, and their product needs to be 18, and their sum needs to be -9.

• Factors of 18 are 1,2,3,6,9,18.

• Which two numbers add to -9 and multiply to 18.

• They are -3 and -6.

• We get (x-3) (x-6).

• -3 multiplied by -6 is equal to 18, and -3+(-6)is equal to -9!

 

Video for better understanding...

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Try these and factor is possible...

1) x^2+6x+5

2) n^2+8n+6

3) n^-10n+16

4) r^-7r+10

 

 

 

 

Answers are...

 

 

1) (x+1) (x+5)

2) not possible

3) (n-2) (n-8)

4) (r-2) (r-5)