Math: factoring decimal trinomials

Tutoring math, I’ve encountered this novelty the last few years.  The tutor suggests one way to see it.

Consider the following:

Factor x2 + 6.7x – 2.1

An interesting problem. As mentioned here, your normal strategy for factoring an easy trinomial would be to find the numbers that multiply to -2.1, but add to 6.7. Behold:

x2 + 6.7x – 2.1 = (x + 7)(x – 0.3)

When you foil it out, you get x2 -0.3x +7x -2.1 = x2 + 6.7x -2.1

However, the times tables don’t cover the numbers that add to 6.7 and mulitply to -2.1; is there a better way?

There’s a trick I use. I’ll show it now, then explain it later.

1) When given x2 + 6.7x – 2.1, imagine x2 + 67x – 210.

2) Use easy trinomial factoring. If you don’t know the numbers that multiply to make -210 but add to 67, make a list starting with 1:

1×210
2×105
3×70

3×70 does it. We know that one number must be negative and one positive, since they multiply to -210.

70-3=67; 70x-3=-210

x2 +67x -210=(x+70)(x-3)

3) Recalling the original question x2 +6.7x – 2.1, we find that (x+7)(x-0.3) is the solution. Notice that we take the numbers from step 2) and divide both by 10: 70÷10 = 7, and -3÷10 = -0.3

This handy trick will get you through most such decimal factoring questions.  Just knowing the pattern, you don’t really need to know why it works.  For those who still want to know why, I’ll explain it in a future post:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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