As a math tutor, you teach and review this method constantly.
Back in May, I began a series of posts about factoring polynomials. To refresh the topic, you can check here, here, and here.
Factoring polynomials is a make-or-break skill for high school students taking academic math. It encompasses about five techniques, of which easy trinomial factoring is probably the best known. Let’s have a quick look:
Example 1: Factor x2 -3x -28
Solution: Since the coefficient of x2 is 1 (which we know because there is no number written in front of it), we can use the easy trinomial method.
Step 1: Write (x )(x )
Step 2: After the x’s, write the numbers that will multiply to give -28, but add to give -3.
You have to do some mental math: 7×4=28, but one of the numbers has to be negative to give -28. The numbers must be -7 and +4, since -7+4=-3.
(x -7)(x +4)
The answer is (x – 7)(x + 4). You can verify using the foil method:
Last: -7*4=-28 (remember: negative times positive gives negative)
Now, line up the four terms we just obtained:
x2 +4x -7x -28
We can combine the like terms: 4x – 7x = -3x
Finally we get
x2 -3x -28.
If you foil out your answer and get back the original trinomial, you know it’s right.
Example 2: Factor x2 + 5x + 4
Solution: The numbers that multiply to give 4 but add to give 5 are 1 and 4: 1*4=4, 1+4=5.
Therefore, the answer is (x + 4)(x + 1)
Example 3: Factor x2 -10x + 16
Solution: The numbers that multiply to give 16 but add to give -10 are -8 and -2 (recall that negative times negative gives positive): -8*-2=16, -8+-2=-10
The answer is (x – 8)(x – 2)
Example 4: Factor x2 +5x – 14
The answer is (x + 7)(x – 2)
Good luck with this method. Most people like it once they get used to it:)
Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.