This week we learned how to use the box method to factor trinomials that didn’t have a leading coefficient of 1 (ugly trinomials). For me, the box method is nice because it doesn’t require me to do as much thinking in my head as the inspection method.
As an example, if you have the expression these are the steps to factor it.
1. Draw a box and split it into quarters so that there are four spaces inside.
2. Write the first term () in the top left-hand corner and write the last term (10) in the bottom right-hand corner.
3. Multiply the two numbers without the variable (30) and find the factors of that number that add up to the middle term (11).
4. Look which numbers already inside the box have corresponding factors or things in common and place them in the two leftover spots. After, add in the variable to the numbers.
5. Find out which numbers multiply to get the numbers in the box and put them on the outside spaces accordingly. It works like a multiplication table.
6. Once you’re done, write the answer in parentheses (3x+5)(x+2)
This week we learned how to factor polynomials. This means that you would take an answer to a FOIL question and find out what the question was. For example, if you take you would first write down all the factors of 49. After that, find the pair of factors that adds up to 14 (7×7). Finally you would write the answer as two binomials (x+7)(x+7).
If you have an expression with two terms () that means that if it were factored, the expression would be conjugates. For example, (x+5)(x-5) are conjugated because the two constants have opposite signs (+ and -). This also means that if you multiply out the expression the +5 and -5 would cancel out and become deep pairs.
This week I learned how to solve problems using double distribution. If you have a question, for example: (2x-3)(2x-3) instead of multiplying the numbers inside the brackets seperately and then multiplying the two numbers left over, you would need to multiply each of the numbers in the first brackets with the ones in the second. You would also have to multiply it in this order: First numbers, outside numbers, middle numbers then the last numbers. The steps should look like this:
- First numbers: Multiply 2x and 2x
- Outside numbers: Multiply 2x and -3
- Middle numbers: Multiply -3 and 2x
- Last numbers: Multiply -3 and -3
When you put it together, it should be -6x-6x+9
Then you can simplify it to -12x+9
This week I learned what the “angle of elevation” was. It is the angle that determines how much rotation something has to undergo to reach a certain point. For example, if there was a person standing on the ground who was looking up at a plane, the angle their eyes needed to rotate up to see the plane would be the angle of elevation.
To find the angle of elevation, you can use SOH CAH TOA. For example, if there was a triangle who’s opposite and adjacent sides measured 29.3 and 16.2, you could use inverse tangent of the opposite side divided by the adjacent. You would then get an angle of 61° which would be your angle of elevation.
This week, we learned about trigonometric ratios. I learned that each side of a triangle in relation to a certain point has a specific name. For example, the side that is right next to the point is called the adjacent side, the longest side of the triangle is called the hypotenuse and the last side is called the opposite side.
The ratios we learned were sine, cosine and tangent. The since ratio is opposite over hypotenuse, the cosine one is adjacent over hypotenuse and the tangent one is opposite over adjacent.
Something I learned in math this week was how to write scientific notation. For example, if you want to write 527000 in scientific notation, it becomes 5.27 ×
You would put the decimal after the first number and then the numbers that come afterwards (that aren’t 0). Then you count how many decimal places the decimal has moved and then use that as the exponent for 10.