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Factoring quadratic trinomials

When asked to factor a quadratic equation such as 2x^2 - 7x -15, many students are uncomfortable with the guess and check method. I created this video to describe a 7 step method that requires NO GUESSING.

Comments

This is terrific!  Thanks so much.
Bonnie
Thank you Bonnie.
It takes a long time and much effort to make these videos and it motivates me to do more when I get positive feedback.
Please use the video any way you think it will help people teach or learn.
Steven G
I am doing "solving quadratic equations by factoring" and "zero product property"...
in all the examples of factoring, they do NOT have any with fractions - so i'm not sure what to do first.
 
Can you help me to find the solution set for this : 4/5x2 = 2x - 4/5
 
I've tried this: 4/5x2 - 2x +4/5 =0  but now i'm sure what to do next...do I factor or get rid of the fraction part?
Jason,
The technique in the video works only when the binomial factors include integers.
Here is how I solved the problem you listed.
Multiply by 5/4 to get x2- (5/2)x + 1 = 0
Use the quadratic formula to get x = 1/2, 2
(x - 1/2)(x - 2) = 0
Steven
(4/5)x2 - 2x + (4/5) = 0
 
The "common denominator" is 5. So multiply both sides by 5"
 
4x2 - 10x + 4 = 0
 
Since you can get the original equation back by dividing both sides by 5,
both equations must have the same solution set. But this equation is
better since it has no fractions in it.
 
You may notice that 4, 10, and 4 have a common divisor of 2.
If you want to use the quadratic formula, then let a = 4, b = -10 and c = 4.
 
10 ± √((-10)2 - 4(4)(4))
---------------------------
2(4)
 
10 ± √(100 - 64)
-------------------
8
 
 
10 ± 6
-------
8
 
2, 1/2
 
 
 
But it would really simplify the arithmetic if you divided both sides by 2 first.
 
2x2 - 5x + 2 = 0
 
Now you can let a = 2, b = -5 and c = 2:
 
5 ± √((-5)2 - 4(2)(2))
-------------------------
 2(2)
 
5 ± √(25 - 16)
-----------------
4
 
5 ± 3
------
4
 
2, 1/2
 
 
You can also factor
2x2 - 5x + 2 = 0
(x - 2)(2x - 1) = 0
x-2 = 0 or 2x - 1 = 0
x = 2, x = 1/2