Worksheet:Quadratic Expand and Factor Skill Sheet
Review 
Let’s expand 
:
We notice that 
gives us the 
; and that 
gives us the constant 
.
To factor a trinomial of the form , we need two values 
such that 
and 
.
Example:
The factor pairs of 54 are (1,54); (2,27); (3,18); (6,9). Now the last pair has a difference of 3, which is what we need for the middle term.
Let 
and 
because 
and 
.
Then,
Factor 
, where 
Example 1:
First, let’s examine the expansion of a factored trinomial of this form:
.
This time, notice that 
as expected, but 
. Rather, 
.
Instead of looking for two numbers that add to 17 and multiply to 10, we need to look for two numbers that add to 17 and multiply to 30.
Example 2:
Factor:
Look for two numbers, 
and 
, such that 
and 
.
The factor pairs of 40 are: (1,40); (2,20); (4,10); (5, 8)
To make 22, we need to use the pair (2,20).
We write a new line of work:
(It doesn’t matter if you write the 
first or the 
first).
Now we look for a common factor in the first two terms:
Perhaps suprisingly, (explained here), let’s look at the last two terms;
Ha! 
is a common factor! Put together we have:
Taking out as a common factor, we have:
Example 3:
Find two numbers, and such that 
and 
.
Factor pairs of 24 are (1,24); (2,12); (3,8); (4,6). Now 
so let 
and 
.
Decomposing the middle term we have:
Grouping we have:
Completing we have
.
Example 4:
First, we notice that all three terms share a common factor 3. Let’s factor this out:
Now we factor the reduced trinomial 
; however the 
is kept present throughout. You might also try factoring without reducing to see how the result compares.
Now we look for and such that 
, and 
.
Factor pairs of 8 are (1, 8); (2, 4). To also satisfy , we need to use 
and 
.
Decomposing we have
Grouping gives
Completing we have
Try it out:
Correct fields show as green, incorrect as red.
Geogebra link to the old applet
Geogebra link to this applet, for full screen capability
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