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Tag Archives: Burtonmath10
Pattern’s in Polynomials
The equation that we must factor is x^2-3x-18!
As we can see, when we fill out the equation is algebra tile form we can see that the algebra tiles are not completely completed. There is a large gap that is missing! This is could be from a possible positive – negative equation that caused a section of the tiles to be cancelled out.
Now we must find out what that other missing number and the other hidden numbers (that are hiding within these numbers) are. As we can see, the (-)18 is a negative number which would mean that the equation to make this number would have to be a (+) positive and (-) negative.
The -18 represents the product of all numbers which would mean that it would be (+)____ x (-)____. And the -3x represents the sum of all numbers which would be (+)____ + (-)_____.
in order to find the numbers that when multiplied equal -18 and when added equal -3, I made a list of all possible numbers that can multiply into -18. Once I had them all down I then added them all together to see which ones would equal -3. I finally found that -6 and 3 both qual -18 when multiplied and -3 when added!
So now that we know that our numbers are x^2,-6,3 and 18. We can the complete the table!
now all we have to do is fill to the outside of the grid with the applicable algebra tiles! We know that a (+)(+)=(+), that (-)(+)=(-), that(-)(-)=(+), that (x)(x) equals x^2, that (x)(1)=1x and that (1)(1)=1!
In the end we end up with (x-6)(x+3) as the factor of x^2-3-18!
This shows pattern because in every equation you always have negatives and negatives equal positive, positive and positive equals positive and negative and positive equals negative. Also, with factoring we see that you must always find the sum of all numbers to equal a number and a variable (ex/4x) and the product of all numbers to equal the lonesome number (ex/12). Also with the algebra tiles all the small squares in the bottom right corner along with the fact that the majority of negative tiles are on the lower half of the grid!
Week 9 – Math 10
my “aha” moment this week is when we learned about a quick and easy way to expand and simplify these binomials! *I’ll be doing the first question* The first step you must do is take the two x’s and multiply them together making it x^2. Then you take the 2 and the 4 and add them together to make 6, which would then give you 6x because (2x+4x=6x). Then you finally take 2 x 4, which gives you 8. Then finally your final answer will be, x^2+6x+8 !
Solving Trig Equations
https://youtu.be/O8VMgBZiUMY
Week 4 – Math 10
I found this question very interesting because this was the first time I came across scientific notation! Scientific notation is where there is only one number before the decimal point. So in order to make 27.1 x 10^4 into scientific notation I had to move the decimal one place to the left. When you move a decimal one place to the left you are in fact adding a positive exponent to the 10^4 (If you were moving it to the right then you’d be adding a negative exponent). Which means that 10^4 is now 10^5. So now we have the number 2.71 x 10^5 (scientific notation form). Though we are not done yet, we need to figure out the value of a + n (a x 10^n). Meaning that we need to addition 2.71 (a) and 5 (n), which gives us 7.71!
Week 3 – Math 10
I really enjoyed learning rational exponents because they seemed very difficult though in reality they are very simple to understand. For this question I took the 3 (denominator) and made that into a cubed root (using flower power). I then put the 125 as the radicand and the 1 (numerator) as an exponent for 125. The next step I did was that I found the cubed root of 125, which is 5 (because 5•5•5=125). Then finally I had 5 to the power of 1 that was left, which is 5. So 125 to the power of 1/3 is 5!
Week 2 – Math 10
I learned to convert mixed radicals with variables into an entire radical. I was quiet confused until I later found out that it is pretty much the same thing as what I learned before. What I did is I took 6 to the power of 2 (using the index as an exponent for 6), which became 36. Then I brought it under the root symbol beside the radicand. Usually I would multiply the 36 and the ‘y’ (radicand) together, though because I do not know the amount of ‘Y’ I left it beside it. In the end I ended up with square root 36y.
Week 1 – math 10
i had an ‘ah ha’ moment when we were working with mixed radicals. I did not realize that there is an imaginary index of 2 and the top right hand of the coefficient. I was stumped on multiple questions that had a coefficient infront of the radicand. Though I then figured out once breaking down the equation into sets that I still had to square root it!