Tuesday, February 10, 2009

Algebra 2: Factoring Trinomials (Part 1)


Ok, so I guess it should really be titled Algebra 1, not 2. But my students always need to review/relearn this topic. We'll go easy for the first lesson - only problems where the GCF = 1 and where the leading coefficient is 1. I made a puzzle for them to put together so that it is more fun than just doing a worksheet. I did something like this in the past with my honors class (but with much harder polynomial equations) and they really enjoyed it. That puzzle, once assembled, instructed them to do push-ups to get some candy. This one only requires that they tell me a joke - I'll add them to my arsenal if they're any good.

Lesson 5 (Factoring Trinomials 1)
Puzzle (doc / pdf)

You may also be interested in the puzzle-based Treasure Hunt I did a couple years ago in Algebra 2.

6 comments:

Daniel Springer said...

here is a really simple way to "factor" trinomials (or solve them).

Consider: x^2+9x-22=0
Then,
x(x+9)=22
This says,
a pair of numbers differ by 9 and have a product of 22.

The two pairs that work are:
{9 and 11} and their opposites {-9 and 11}

We take the smaller of each pair since x is smaller than x + 9

Thus, x = 9 or -11.

The method really shines when the quadratic coefficient is not 1.

Example..

6x^2-7x-5=0
By mult. by 6 and factoring we write..
6x(6x-7)=5*6
-->differ by 7, product = 30
pairs are {10 and 3} and {-10 and -3)
6x is larger than 6x-7-->we take the larger.

x = 10/6 or -3/6

We divided by 6, since the pair represented 6x, not 6

Nick said...

Dan - I'm pretty sure I've at some point decided that you use grapher to make your visuals. Like the little summary images you include with most posts - is that correct? They often look great. I can't get something as simple/nice in geogebra, and PSTricks is often the looooooooooooong way.

Dan Greene said...

Yep, Grapher it is. It can be a bit of a pain to work with in certain ways, but it usually makes nice images.

Nick said...

Is it just me or are there a few typos here... A few minutes later, I think it's just me. Well... I'm gonna give the puzzle a go, I'll report back on how it fares - thanks for offering it up.

Dan Greene said...

Nick, if you find any typos, please let me know, and I'll fix them right away. I hope the puzzle goes well for you.

DWees said...

Yeah your puzzle is cool. So cool that I've created a random generator in Adobe Flex.

See my algebra puzzle generator.