What's up guys, it's Amy. Hope you've had a good day, or night by the time this goes up (sorry for the late posting). I'll be combining yesterday and today in this blog post, since we had only had work time yesterday. So basically, yesterday was a pretty cool day. We had some Kobe exchange students sit in with us for a bit, we reviewed Karmen's blog post, talked about different reflections we can put on our blog (ie. Math/Science facts, interesting discoveries, wellness) and it was Pi day too! Since yesterday was Pi day, we watched a couple Vihart Pi day youtube videos, and talked a bit about Pi and how it's the worst. Quick fun fact that isn't so fun but kinda sad: According to CBC, only 50% of adult's are able to read and understand a simple line graph. Shoutout to Sheyda for that fact, and also for a very interesting reflection on the life of Stephen Hawking that was made to acknowledge his passing yesterday. Today, our first topic was Binomial Common Factors. When we are factoring binomials, we need to find the common factor. This means that out of our equation, the part that is repeated is the common factor. After we have found the common factor, we will need to start to factor the equation. Therefore, we want to put the common factor at the beginning of the equation, and that will be followed by the remaining. After this, we will need to find the GCF (greatest common factor) of the remaining. The GCF will be separated and multiplied out to form the original remaining. Once this is done, the GCF will be put at the beginning of the equation. Meaning that the fully factored equation would be, the GCF followed by the common factor, and lastly the multiplied out remaining. Ex: |
Hello everyone! It's Megan J here again, but this time with multiplying polynomials! But, before we get onto that, it was Chloë's appreciation day today! Congrats Chloë! | Here's a video that I found helpful and quite amusing: |
So, the acronym 'FOIL' stands for 'First Outside Inside Last', which is the order that you multiply the two polynomials to get the final polynomial.
For example, if I had to multiply the polynomials (4x+3y)*(2x-8x) and then simplify it afterwords, I would multiply 4x*2x (first) then 4x*-8x (outside) then 3y*2x (inside) then 3y*-8x. On your test you might write it something like this.
(4x+3y)*(2x-8x)
(4x*2x)+(4x*-8x)+( 3y*2x)+(3y*-8x)
8x²-32x²+6xy-24xy
Now, once you've gotten to this stage, you'll want to combine like terms, so it would look like this:
-24x²-18xy
And that's your final answer!
For example, if I had to multiply the polynomials (4x+3y)*(2x-8x) and then simplify it afterwords, I would multiply 4x*2x (first) then 4x*-8x (outside) then 3y*2x (inside) then 3y*-8x. On your test you might write it something like this.
(4x+3y)*(2x-8x)
(4x*2x)+(4x*-8x)+( 3y*2x)+(3y*-8x)
8x²-32x²+6xy-24xy
Now, once you've gotten to this stage, you'll want to combine like terms, so it would look like this:
-24x²-18xy
And that's your final answer!
Another way to multiply polynomials is by using the tic tac toe FOIL method:
After multiplying, your product would look like this:
-x²+3x+8x-24
Once you've combined like terms, you'll have your final answer which is:
-x²+11x-24
And there you have it! Two simple ways of multiplying polynomials.
-x²+3x+8x-24
Once you've combined like terms, you'll have your final answer which is:
-x²+11x-24
And there you have it! Two simple ways of multiplying polynomials.
Hi!
This lesson spanned over two days, sorry for such a late update(this is Emma btw). The class started with a hectic chase after Mr. Joliff and some really neat info about the challenge IS projects. We also learned a bit about the Desmos project that's coming up later this semester, it's where you choose a picture, could be a logo could be a drawing, and you graph it using the program desmos, it seems really cool and I'm definitely looking forward to it.
In this lesson Ms. B talked about counting the degrees of polynomials and how to put it in degree order and how to classify polynomials. We also worked with subtracting polynomials and also just a general refresher because I think some may have forgotten bits of this unit(I know I DEFINITELY have) seeing as it was over a year ago. That being said, Ms. B is always really really great at explaining stuff if you have questions, like trust me, I speak from experience (she hasn't gotten tired of me asking questions, even the ones that are quite, shall we say, elementary)
Going back to the Desmos topic, we had some really cool demonstrations by Ms. B on the platform and I don't know about y'all, but I (as mentioned before) am really really looking forward to it. There is also a new classroom that Ms. B set up if you are interested in future opportunities that have criteria, idk if that makes sense, but basically, if you're interested in learning about scholarships and all around cool opportunities check it out. The classroom code is n88vzcm.
Some multimedia to check out. The first video(bottom left) is a bit simplistic and covers some of the stuff we already know(and its a bit long), but I thought it explained everything very clearly great way(imo, it may not be for everyone though) . The second video is much shorter and it assumes you know the "standard form" to write polynomials(from the highest to the lowest degree), he talks a bit quickly, but I liked how he brought in the names for each of them(ex: cubic polynomial w/ 4 terms).
This lesson spanned over two days, sorry for such a late update(this is Emma btw). The class started with a hectic chase after Mr. Joliff and some really neat info about the challenge IS projects. We also learned a bit about the Desmos project that's coming up later this semester, it's where you choose a picture, could be a logo could be a drawing, and you graph it using the program desmos, it seems really cool and I'm definitely looking forward to it.
In this lesson Ms. B talked about counting the degrees of polynomials and how to put it in degree order and how to classify polynomials. We also worked with subtracting polynomials and also just a general refresher because I think some may have forgotten bits of this unit(I know I DEFINITELY have) seeing as it was over a year ago. That being said, Ms. B is always really really great at explaining stuff if you have questions, like trust me, I speak from experience (she hasn't gotten tired of me asking questions, even the ones that are quite, shall we say, elementary)
Going back to the Desmos topic, we had some really cool demonstrations by Ms. B on the platform and I don't know about y'all, but I (as mentioned before) am really really looking forward to it. There is also a new classroom that Ms. B set up if you are interested in future opportunities that have criteria, idk if that makes sense, but basically, if you're interested in learning about scholarships and all around cool opportunities check it out. The classroom code is n88vzcm.
Some multimedia to check out. The first video(bottom left) is a bit simplistic and covers some of the stuff we already know(and its a bit long), but I thought it explained everything very clearly great way(imo, it may not be for everyone though) . The second video is much shorter and it assumes you know the "standard form" to write polynomials(from the highest to the lowest degree), he talks a bit quickly, but I liked how he brought in the names for each of them(ex: cubic polynomial w/ 4 terms).
| |
"Where do cubes born?"
-Kain
Hey y'all, Nathaniel here
Today we did perfect squares and cubes, and basic radical notation and use. Let's start with a couple definitions. A radical is any number with a root function around it, for example √23 or ∛27, a perfect square is any number that can be represented as a square with the same integer as its side lengths, and similarly a perfect cube is any number that can be represented as a cube with the same integer as its side lengths. For example, √9 = 3, 3² = 9, ∛27 = 3, and 3³ = 27. 9 is a perfect square because it can be represented as 3², and 27 is a perfect cube because it can be represented as 3³.
At some point you may have realized that the question x^2 = 25 has two possible answers, 5 and -5, and so we need to do a little math maneuvering. If you equation looks like this, √25 = x, the answer will always be +5, this is called the principle root. If your equation looks like this however, x^2 = 25, you don't know if the answer is + or -, so you would write x = ±5. This symbol, ±, means that the answer could be either positive or negative.
We also covered how to find a square root and cube root, and how to use the volume of a cube to find its surface area, and vice versa.
To find a square root: Find √16 Use prime factorization like so Prime factors of 16 are 2, 2, 2, 2 separate the prime factors into two groups like so 2, 2 2, 2 Then you can multiply factors in each group together to get 4 and 4, and then you have your answer 4^2 = 16 √16 = 4 | To find a cube root: find ∛512 Use prime factorization Prime factors of 512 are 2, 2, 2, 2, 2, 2, 2, 2, 2 Separate them into three groups like so 2, 2, 2 2, 2, 2 2, 2, 2 Then multiply the factors on each group to get 8, 8, 8 Therefor 8^3 = 512 ∛512 = 8 | To find Surface Area from Volume of a cube and vice versa: s = side length of a cube V = volume of a cube SA = Surface area of a cube V = s^3 SA = 6s^2 s = ∛V s = √(SA/6) Therefor your final equation would be 6(∛V)^2 = SA if you have volume, and your final answer would be (√(SA/6))^2 = V if you have surface area |
Hope that helped a little :) | Here's a woman explaining how to find square roots from factor trees: |
Hey guys, it’s Amelia, I’ll be doing a brief overview of what we learned over the past two days on our new unit; factors and products. We went over how to use a factor tree and division tables to find the factors of a product. And then we learned to find the Greatest Common Factor (which we refer to as GCF) and finding the Least Common Multiple (which we refer to as LCM).
- We first went over factor trees which is a pretty simple concept to grasp. Factor trees is useful to find the factors that go into making a product.
- We then learned how to use division table to find the factors that make a product. Its just another method to use if using a factor tree doesn’t work for you.
- Next we learned about finding the Greatest Common Factor; GCF and the Least Commom Multiple; LMC. This picture shows very simple way of doing them.
Here’s a video to help you guys understand GCF and LCM
Hope this helped y’all out! There was no homework assigned and just a reminder the trig test is this Tuesday!
Author
We are the students of FPC Math 10C.
Where are you from? Find your green dot!
Archives
June 2018
May 2018
April 2018
March 2018
February 2018
January 2018