This week in math I learned how to factor binomials with perfect squares. To factor one, one of the terms has to have a negative.

For example: 36x^2 – 9^2

To solve this, first you would need to take the square root of 36 and x in the beginning of both brackets-> (6x    )(6x     )

Then you would put the square root of 9 at the end of the brackets-> (6x   3 )(6x   3)

In between the two, one sign needs to be positive and one needs to be negative so that they cancel out-> (6x + 3 )(6x – 3)

You can always FOIL your answer to check if it’s right.

More examples:

This week we worked on polynomials and I learned how to apply the distributive law when multiplying.

If your equation was 7x(2-3) you would have to distribute the 7x to everything in the brackets, so multiply the 7x by 2 and -3. The expanded form should be 14x-21x. Then you would collect the like terms and the simplified answer would be -7x.

If you were working with two sets of brackets, you would do the same thing, except distribute more than one term.

Don’t forget to add the exponents together when you are multiplying.

Here are some examples:

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This week in Math 10 I learned what the angle of elevation and the angle of depression is on a triangle. These angles are usually in word problems and can be found the same way you would find any other angle. (By labelling your triangle, then using either Sine Cosine or Tangent to solve for x.)

The angle of elevation is found between the horizontal line and the slanted line that goes up (also called line of sight).

The angle of depression is found on the opposite side of the angle of elevation. It is the angle between the vertical line and the line of sight.

Here are some visuals:

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This week in Math 10 I learned what the mnemonic device SOH CAH TOA means. It is something that is very helpful to use to remember the definitions of the trigonometric functions sine, cosine and tangent.

First we can figure out how to find sine by doing the opposite angle divided by the hypotenuse. Since the O goes before the H in SOH, it means O is the number on the top of the fraction (division).

To find cosine we would do the adjacent side divided by the hypotenuse, since the A in CAH goes before the H.

To find tangent we would do the opposite side divided by the adjacent side, since the O goes before the A in TOA.

The first letters- S, C and T are just there to tell you what function it would be (sine, cosine, tangent).

SOH CAH TOA should be the first thing you write on your paper since it is very helpful, then you should label all the sides of the triangle.

Here is an example of me using SOH CAH TOA to help me find a missing side of a triangle:

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This week in Math 10 I learned how to find the hypotenuse, opposite and adjacent side of a triangle.

To find the hypotenuse you find the longest side of the triangle, it is also the side opposite of the 90 degree angle.

To the find the opposite side of the triangle you start at the theta angle. (Theta is a greek letter, used as a variable to indicate an angle, in this case the reference angle). The side that is opposite of theta is called the opposite.

To find the adjacent you look at the last side left, that is also always beside theta.

Here are some examples:

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This week in Math 10 I learned about the zero exponent rule. It means that any number or variable that is raised to the power of 0 equals 1. This is because the exponent tells you how many copies of the base there are (number in front of exponent) and since there are 0 copies of the base, you would think that means the answer is 0.

No, there is a coefficient in front of the base which is not written, it’s 1.

Here is an example:

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If there already is a coefficient (number in front of base) then the answer will be that. Since the base would just be 1 and you would be multiplying the coefficient by 1.

Here is an example:

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This week in math I learned how to do factor trees. This is a type of diagram that shows the different factors of a number and helps to find the prime factorization. Prime factorization is finding which prime numbers multiply together to make the original number. (Prime numbers are numbers that only have 2 factors, 1 and itself).

It starts with the number you want to find the factors of at the top, then has two branches (lines) below. Under these branches you write the original numbers’s factors and continue doing the same thing over again until you reach a prime factor. Once you get to a prime factor you circle it and don’t add any branches to it.

This is a good way to find the prime factorization of a number especially if the number is not too big. If the number is too big it might take some time and be harder to find factors for it but it’s still possible.

Here are some examples of factor trees:

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