Factoring Polynomials - FREE Worksheet

Filed in Algebra and written by
Email
Print

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:

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:

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!

then
or
You might also like:



This post may contain affiliate links. When you use them, you support us so we can continue to provide free content!

MathFourNewsletter
If you enjoyed this post, please consider leaving a comment or subscribing to the RSS feed to have future articles delivered to your feed reader.
4 Awesome Comments! - Leave a comment or ask a question about this
4 Responses to Factoring Polynomials - FREE Worksheet
  1. Colin Beveridge

    Oo, pick me, pick me!

    There's a quick way to find the missing magic numbers -- find the factors of (ac) that add up to (b) -- so for 6x^2 + 65x + 50, you'd look at 300; the possibilities are 1 and 300, 2 and 150, 3 and 100, 4 and 75, 5 and 60 (which works), 6 and 50, 10 and 30, 12 and 25, or 15 and 20.

    It's a little bit more work up front, but it saves you doing several grids.
    Colin Beveridge recently posted..Quotable maths: Roberts

    Reply
    • Bon

      I think that may be the point, Colin. That method totally works for you (I'm guessing) - but it sends me into panic mode.

      My major prof in grad school trained me to "get my hands dirty" (he'd tell me that ALL THE TIME). So now I write every single detail out.

      And for our students - whatever works for them, should be what they use.

      Thanks for stopping by!

      Reply
  2. Cristina

    This is an interetsing method… I didn't come accros it before… I like it! Do share more :-)
    Cristina recently posted..ThoughtBox wins Blueface Business Elevator Final

    Reply
    • Bon

      Thanks, Cristina! I'll happily pass along things as I find them. :)

      Reply
Leave a Reply

Wanting to leave an <em>phasis on your comment?

CommentLuv badge
Trackback URL http://mathfour.com/algebra/factoring-polynomials-free-worksheet/trackback

Factoring Polynomials - FREE Worksheet

Filed in Algebra and written by
Email
Print

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:

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:

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!

then
or
You might also like:



This post may contain affiliate links. When you use them, you support us so we can continue to provide free content!

MathFourNewsletter
If you enjoyed this post, please consider leaving a comment or subscribing to the RSS feed to have future articles delivered to your feed reader.
4 Awesome Comments! - Leave a comment or ask a question about this
4 Responses to Factoring Polynomials - FREE Worksheet
  1. Colin Beveridge

    Oo, pick me, pick me!

    There's a quick way to find the missing magic numbers -- find the factors of (ac) that add up to (b) -- so for 6x^2 + 65x + 50, you'd look at 300; the possibilities are 1 and 300, 2 and 150, 3 and 100, 4 and 75, 5 and 60 (which works), 6 and 50, 10 and 30, 12 and 25, or 15 and 20.

    It's a little bit more work up front, but it saves you doing several grids.
    Colin Beveridge recently posted..Quotable maths: Roberts
    Colin Beveridge recently posted..Quotable maths: Roberts

    Reply
    • Bon

      I think that may be the point, Colin. That method totally works for you (I'm guessing) - but it sends me into panic mode.

      My major prof in grad school trained me to "get my hands dirty" (he'd tell me that ALL THE TIME). So now I write every single detail out.

      And for our students - whatever works for them, should be what they use.

      Thanks for stopping by!

      Reply
  2. Cristina

    This is an interetsing method… I didn't come accros it before… I like it! Do share more :-)
    Cristina recently posted..ThoughtBox wins Blueface Business Elevator Final
    Cristina recently posted..ThoughtBox wins Blueface Business Elevator Final

    Reply
    • Bon

      Thanks, Cristina! I'll happily pass along things as I find them. :)

      Reply
Leave a Reply

Wanting to leave an <em>phasis on your comment?

Trackback URL http://mathfour.com/algebra/factoring-polynomials-free-worksheet/trackback

Factoring Polynomials - FREE Worksheet

Filed in Algebra and written by
Email
Print

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:

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:

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!

then
or
You might also like:



This post may contain affiliate links. When you use them, you support us so we can continue to provide free content!

MathFourNewsletter
If you enjoyed this post, please consider leaving a comment or subscribing to the RSS feed to have future articles delivered to your feed reader.
4 Awesome Comments! - Leave a comment or ask a question about this
4 Responses to Factoring Polynomials - FREE Worksheet
  1. Colin Beveridge

    Oo, pick me, pick me!

    There's a quick way to find the missing magic numbers -- find the factors of (ac) that add up to (b) -- so for 6x^2 + 65x + 50, you'd look at 300; the possibilities are 1 and 300, 2 and 150, 3 and 100, 4 and 75, 5 and 60 (which works), 6 and 50, 10 and 30, 12 and 25, or 15 and 20.

    It's a little bit more work up front, but it saves you doing several grids.
    Colin Beveridge recently posted..Quotable maths: Roberts
    Colin Beveridge recently posted..Quotable maths: Roberts
    Colin Beveridge recently posted..Quotable maths: Roberts

    Reply
    • Bon

      I think that may be the point, Colin. That method totally works for you (I'm guessing) - but it sends me into panic mode.

      My major prof in grad school trained me to "get my hands dirty" (he'd tell me that ALL THE TIME). So now I write every single detail out.

      And for our students - whatever works for them, should be what they use.

      Thanks for stopping by!

      Reply
  2. Cristina

    This is an interetsing method… I didn't come accros it before… I like it! Do share more :-)
    Cristina recently posted..ThoughtBox wins Blueface Business Elevator Final
    Cristina recently posted..ThoughtBox wins Blueface Business Elevator Final
    Cristina recently posted..ThoughtBox wins Blueface Business Elevator Final

    Reply
    • Bon

      Thanks, Cristina! I'll happily pass along things as I find them. :)

      Reply
Leave a Reply

Wanting to leave an <em>phasis on your comment?

Trackback URL http://mathfour.com/algebra/factoring-polynomials-free-worksheet/trackback

Factoring Polynomials - FREE Worksheet

Filed in Algebra and written by
Email
Print

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:

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:

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!

then
or
You might also like:



This post may contain affiliate links. When you use them, you support us so we can continue to provide free content!

MathFourNewsletter
If you enjoyed this post, please consider leaving a comment or subscribing to the RSS feed to have future articles delivered to your feed reader.
4 Awesome Comments! - Leave a comment or ask a question about this
4 Responses to Factoring Polynomials - FREE Worksheet
  1. Colin Beveridge

    Oo, pick me, pick me!

    There's a quick way to find the missing magic numbers -- find the factors of (ac) that add up to (b) -- so for 6x^2 + 65x + 50, you'd look at 300; the possibilities are 1 and 300, 2 and 150, 3 and 100, 4 and 75, 5 and 60 (which works), 6 and 50, 10 and 30, 12 and 25, or 15 and 20.

    It's a little bit more work up front, but it saves you doing several grids.
    Colin Beveridge recently posted..Quotable maths: Roberts
    Colin Beveridge recently posted..Quotable maths: Roberts
    Colin Beveridge recently posted..Quotable maths: Roberts
    Colin Beveridge recently posted..Quotable maths: Roberts

    Reply
    • Bon

      I think that may be the point, Colin. That method totally works for you (I'm guessing) - but it sends me into panic mode.

      My major prof in grad school trained me to "get my hands dirty" (he'd tell me that ALL THE TIME). So now I write every single detail out.

      And for our students - whatever works for them, should be what they use.

      Thanks for stopping by!

      Reply
  2. Cristina

    This is an interetsing method… I didn't come accros it before… I like it! Do share more :-)
    Cristina recently posted..ThoughtBox wins Blueface Business Elevator Final
    Cristina recently posted..ThoughtBox wins Blueface Business Elevator Final
    Cristina recently posted..ThoughtBox wins Blueface Business Elevator Final
    Cristina recently posted..ThoughtBox wins Blueface Business Elevator Final

    Reply
    • Bon

      Thanks, Cristina! I'll happily pass along things as I find them. :)

      Reply
Leave a Reply

Wanting to leave an <em>phasis on your comment?

Trackback URL http://mathfour.com/algebra/factoring-polynomials-free-worksheet/trackback