Factoring Trinomials a = 1 Lesson

Factoring Trinomials with Leading Coefficient of 1

In the form:

 $x^2\pm bx\pm c$  

To Factor a trinomial:

• Remember to always check for a GCF first!

• If there is one, pull it out and write it on the outside of the (). Then continue to factor.

• For trinomials with leading coefficient of 1, find factors of the constant (c) that add to the middle (b) value

• Place those 2 factors in two sets of ( ). Watch your signs!

• You can FOIL (multiply out) to check your answer

Multiple Choice

Quick Check:  

In order to factor a trinomial in the form:

 $x^2+bx+c$  we need to find 2 factors of  $c$  that.....?

• Add to c

• Subtract to b

• Add to b

• Subtract to c

Multiple Choice

Let's factor:    $x^2+7x+12$       a = 1,  b = 7 and c = 12

First, what are the factors of  12 (c) that add to 7 (b)?

• 3 and 4

• 2 and 6

• 1 and 12

• There are none that add to 7

Multiple Choice

Which is the correct factored form:        $x^2+7x+12$  ?

• (x+3)(x+4)

• (x+2)(x+6)

• (x+7)(x+1)

• (x+12)(x+1)

Multiple Choice

Now let's factor:      $x^2-15x+36$    

First find two factors of $36$  that add to  $-15$  .

• -12 and -3

• 12 and -3

• -4 and -9

• -6 and -6

• -2 and 18

Fill in the Blanks

 Write the 2 binomials that finish factoring:   $x^2-15x+36$  
Do NOT use spaces between anything!

Multiple Choice

Now factor this:     $x^2-4x-32$  Think about which 2 factors of -32 would add to -4.  Select the correct factored form:

• (x - 16)(x + 2)

• (x - 2)(x + 16)

• (x - 8)(x + 4)

• (x - 4)(x + 8)

Now let's factor:

 $3x^2+6x-72$  

• This does NOT have a leading coefficient of 1

• Does it have a GCF?  

• Yes!  We need to factor out the GCF first.

Multiple Choice

What is the GCF of:    $3x^2+6x-72$ ? 

• 6

• 3

• 3x

• There is NO GCF

Multiple Choice

Which is the factored form if we pull out a GCF of 3?      $3x^2+6x-72$  

•  $3\left(x^2+2x-24\right)$  

•  $3\left(x^2+6x-72\right)$  

•  $3\left(x^2+3x-24\right)$  

Multiple Choice

 $3\left(x^2+2x-24\right)$  

Notice the expression inside can be factored further.  Think about factors of -24 that add to  2.  Which is the final factored form?

• 3(x+6)(x-4)

• 3(x-6)(x+4)

• 3(x-8)(x+3)

• 3(x+8)(x-3)

Now try a couple without any help. :)

• Remember to enter your answers without using any spaces.

• Look for GCF and pull out first. Put it on the outside.

• Watch the signs of the factors!

• Make sure they add up to the middle 'b' value!

Fill in the Blanks

Factor:      $x^2-2x-24$  

Fill in the Blanks

Factor:      $x^2+8x-48$  

Fill in the Blanks

Factor completely:        $4x^2-20x+24$   

Write out the fully factored form including the GCF. 

Poll

How do you feel about factoring trinomials with a = 1?

• I got it!

• I'm close!

• Not quite sure.

• Completely lost!