Worksheet:Quadratic Expand and Factor Skill Sheet
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 .
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 .
Factor , where
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.
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:
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
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
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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