Factoring Trinomials Simply

Welcome to my PAGE students!

Factoring trinomials of the form x2 + bx + c is often perceived by many students of a first year course in Algebra as a grand mystery and a topic that leads to much frustration.

So this page is being prepared to provide some help in this topic.

In this website, you are expected to do the following:

1. watch the video or read definitions on how to factor trinomials;

2. practice answering to the given game link on factoring trinomials;

3. answer exercises on factoring trinomials; (to check tomorrow)

4. answer set of equations given with correct answers in a beautilful paper.(to do check next week as part of your project)

ARE YOU READY???

TASK 1

[video:http://www.youtube.com/watch?v=r1JAJfmRG5w width:640 height:640 align:center]

FACTORING IS THE REVERSE of multiplying. 

2x2 + 9x − 5

-- it will be factored as a product of binomials:

(?   ?)(?   ?)

The first term of each binomial will be the factors of 2x2, and the second term will be the factors of 5.

Now, how can we produce 2x2?  There is only one way:  2x· x :

(2x   ?)(x   ?)

And how can we produce 5?  Again, there is only one way:  1·  5.  But does the 5 go with  2x --

(2x   5)(x   1)

or with  x --

(2x   1)(x   5) ?

Notice:  We have not yet placed any signs

How shall we decide between these two possibilities?  It is the combination that will correctly give the middle term, 9x :

2x2 + 9x − 5.

Consider the first possibility:

(2x   5)(x   1)

Is it possible to produce  9x  by combining the outers and the inners:

2x (that is, 2x· 1) with  5x ?

No, it is not.  Therefore, we must eliminate that possibility and consider the other:

(2x   1)(x   5)

Can we produce  9x  by combining  10x  with 1x ?

Yes -- if we choose +5 and −1:

 (2x − 1)(x + 5)

(2x − 1)(x + 5) = 2x2 + 9x − 5.

Skill in factoring depends on skill in multiplying -- particularly in picking out the middle term

TASK 2

Click the link below to practice factoring trinomials.

TASK 3

Problem 1.   Place the correct signs to give the middle term.

a)  2x2 + 7x − 15 = (2x   3)(x   5)

b)  2x2 − 7x − 15 = (2x   3)(x   5) 

c)  2x2 − x − 15 = (2x   5)(x   3) 

d)  2x2 − 13x + 15 = (2x   3)(x   5) 

Problem 2.   Factor these trinomials.

a)  3x2 + 8x + 5  =                            

b)  3x2 + 16x + 5  =                           

c)  2x2 + 9x + 7  =                           

d)  2x2 + 15x + 7  =                            

e)  5x2 + 8x + 3  =                            

f)  5x2 + 16x + 3  =                           

g)  2x2 − 7x + 5  =                          

h)  2x2 − 11x + 5  =                            

i)  3x2 + x − 10   =                            

j)  2x2 − x − 3   =                            

TASK 4

Answer the each equation and copy and answer them in a beautiful paper.

THE END!