Algebra 1 problem -- Typo or is my brain puttering out?

[Gil]

Write the missing value in each trinomial

s^2 - 10s - 20 = (s + 2) (s + [_])

 

I was working with a tutee today and we were going over their homework together. There were several sections on the packet and when we got to this section I could do all of the problems like this one within 5-10 seconds without writing it down but this one stomped me and its bothering me.

 

What am I missing? Is this a typo or is my brain just puttering out on me?

 

(This worksheet DID have a few obvious typos in a couple of other problems.)

[Tsuga]

That is a typo. You can always check by punching it into a calculator:

 

http://www.mathportal.org/calculators/polynomials-solvers/polynomial-factoring-calculator.php

 

I mean don't tell your tutee... ;)

[Arcadia]

Typo error. I am guessing

 

s^2 - 10s - 20 = (s + 2) (s + [_])

 

to be

s^2 - 10s - 24 = (s + 2) (s + [_])

 

and the blank to be -12

[Gil]

Thanks, I thought it was a typo but couldn't accept that it the worksheet was wrong because my brain kept trying figure out which number was supposed to be wrong. (I didn't see it as s^2 - 10s - 24) I kept mentally adjusting for the 10s in the middle.

 

I had graphed it by hand and I used the the quadratic formula on it and I KNEW that the problem didn't make sense. This kid is roughly 2/3 of the way through Algebra 1 but he didn't know how to graph quadratics or use the quadratic formula yet. I wasn't sure how to explain to him how I knew that the worksheet was wrong so I kept looking for how *I* could be wrong.

[mathwonk]

a quick way to check this is wrong is to plug in s = -2 on both sides.  you get zero on the right side where there is  afactor of (s+2), but you don't get zero on the left, you get 4, so to make it work you have to subtract off another 4 on the left.

 

edit:  In my opinion, this is probably the most important principle in algebra, called the "root - factor" theorem.  I.e. given any polynomial f(x), the linear term (x-a) is a factor of f(x) if and only if x=a is a root, i.e. iff f(a) = 0.

Edited January 27, 2016 by mathwonk