Tag: worksheets

  • Factoring Polynomials — FREE Worksheet

    Factoring Polynomials — FREE Worksheet

    In factoring polynomials it’s sometimes handy to break up the work graphically. Lisa Nuss, a member of Sam Shah’s New Blogger Initiation, shared a handy graphic organizer last week.

    I struggle with factoring polynomials, myself, so I wanted to give it a try.

    It started out easy.

    I started factoring polynomials with 1 as the leading coefficient (i.e. x2 has no messy number in front of it).

    I factored:

    \(x^2 + 14x + 48\)

    First, I put the first and last terms in the boxes. (Note that this graphic organizer works the same way as a multiplication table.)

    Then I factored those two in the given “factors” boxes. I determined which factors of 48 would add up to 14, and filled in the chart appropriately.

    I was done with that factorization.

    Yay me!

    Then I got into harder stuff.

    Lisa put in an extra “Factors” box to handle non-unit leading coefficients. So I went for a big dog:

    \(6x^2 + 65x + 50\)

    Here’s how far I got before the breaks squealed:

    Factoring polynomials like this one shouldn’t be too much of a problem. Especially if you use a page protector and a dry erase pen to do the trial and error work, as Lisa suggested.

    But I don’t have such fancy technology.

    And I don’t like to erase my work. I want to see everything I’ve tried. For me, it’s very likely that I make a mistake and have to go back. And it’s a real pain to have to re-create everything.

    So instead of playing trial and error with the one big sheet of paper, I created a Factor Trial & Error Boxes worksheet (or in Lisa’s terminology: a graphic organizer).

    Here’s what my work looked like:

    (It was a coincidence that the right answer was last, by the way.)

    With that info, I could go back to my big graphic organizer and finish the problem.

    This was very pleasing. I was able to use Lisa’s graphic organizer and mine to make sure I didn’t lose any options in my my trial & error.

    Will it work for you and your kids? Download the Factor Trial & Error Boxes worksheet now and give it a shot!

    Share your thoughts in the comments or on twitter/x.

    You might also like:
  • Yummymath for Kids & Cheap Help for Grownups

    Yummymath for Kids & Cheap Help for Grownups

    Daughter is into Goldfish. So much so that my brother has dubbed my car The Goldfish Burial Ground. If my Harry Potter wand worked, I could “poof” my car clean. Alas, Daughter loves Goldfish, and my magic wand is defunct.

    So when Yummymath shared these activities with me, one on Goldfish and one on HP movies, I was pretty excited. They’re long, so they put them in PDF form:

    Notice that, although there are some right and wrong answers, it’s a lot of investigation. Furthermore, in the Harry Potter worksheet, kids get to decide on their own what determines success for a movie. Both great things to do in the world of teaching math.

    Yummymath provides about three or four of these worksheets for free on their website every week. Yes, for free!

    They also provide a parent/teacher help guide…

    …if you’re a member. “Oh yeah, there’s the catch,” I hear you thinking. Indeed, at the whopping fee of $9 dollars per year (yes, per year) you have access to the solutions/help guide for all the exercises.

    Here’s what they look like:

    I’m trying to convince them to up their price. I think it should be a monthly fee. It’s extremely hard to make exercises like these, not to mention all the effort they put into the parent/teacher guide.

    They’ve informed me that they’re likely to go up to $12 per year. ARG

    In the meantime, you probably should get in quick, before I convince them of the amazing value they are offering.

    Oh – and tell me in the comments how you like the exercises and guides – I’d love to hear your feedback!

    UN-Disclaimer: They didn’t give me squat for this article except these exercises to give to you for free. I don’t even get commission on sales. (Not that they could afford it at that ludicrously cheap price!) What they’re doing is great. Yummymath is an awesome resources for homeschool and classroom teachers everywhere!

    Related articles