Category Archives: Math 10

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Week 6 – Math 10 – Multiplying polynomials

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This week we learned how to multiply polynomials in several different ways. In order to multiply polynomials, you need to understand the distributive property and the multiplication exponent law, but I will explain them when they come up. I this I will explain how to multiply a trinomial (3 terms) by a binomial (2 terms) in 2 ways. The example I will be solving is (5x2-3x+6)(4x+5)

 

Way 1: algebraically

First I can start with expanding. Each term in the first bracket will multiply into terms in the second, because of the distributive property. This is what the equation would look expanded:

5x2(4x)+5x2(5)-3x(4x)-3x(5)+5(4x)+5(5)

 

Know I can do the individual multiplication:

20x3+25x2-12x2-15x+20x+20

 

The reason 5x2(4x)=20x3 is according to the multiplication exponent law. There in an invisible exponent of 1 on the 4x.

Before I combine like terms I like to organize my equation to make things easier for myself. I organize the equation by like terms then I combine. This equation is already organized so I can skip that step.

Like terms combined: 20x3+13x2+5x+20

 

Way 2: visually

(5x2-3x+6)(4x+5)

You start with making a box with lines separating it to the number of terms

     
     
     
     

 

Then you fill in the polynomials to their respective sides. put each term on a line like this

  4x 5
5x2    
-3x    
6    

 

Then I would do the multiplication in the individual squares

  4x 5
5x2 20x3 25x2
-3x -13x2 -15x
6 24x 30

 

Know I can right out the hole equation and combine like terms.

Written out: 20×3+25×2-12×2-15x+20x+20

Like terms combined: 20×3+13×2+5x+20

Math 10

Week 5 – Math 10 – Naming Polynomials

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Week 5 – Math 10 – Naming Polynomials

This week in math 10, we learned how to name polynomials based on the number of terms and the degree. This is an example:

2x3 + x2

This this a Binomial because it has two terms. This is a Cubic polynomial because it has a degree of three. The fallowing is a list of the vocabulary with an example of each:

A Monomial has 1 term

X2

A Binomial has 2 terms

2x2 – 4x

A Trinomial has 3 terms

3x2 – 2x + 3

A Polynomial has multiple terms

4x3 + 5x2 + 6x – 7

A Linear polynomial has a degree of 1

4x – 7

A Quadratic polynomial has a degree of 2

6x2 – 2x

A Cubic polynomial has a degree of 3

4x3 + 2x2 – 8

A Quartic polynomial has a degree of 4

6x4 – 7x2 + 5

A Quintic polynomial has a degree of 5

2x5 + 3x3 – 4x + 3

Math 10

Math 10 – week 4 – solving triangles

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This week in math we learned how to solve a triangle. Solving a triangle is much different than solving an equation. When solving an equation, you are trying to find the variable. However, when you are solving a triangle, you are trying to find all of the side lengths and angles.

Tools for solving Triangles:

All angles in triangles add to 180°

Pythagorean Theorem (a2+b2=c2)

SahCahToa (Sin, Cos, Tan)

Here is an example of a triangle that I will solve:

First we can use the Pythagorean Theorem to solve for the hypotenuse (AB)

292+382=C2

841+1444=2285

the answer is the square root of 2285

C=47.8

Now we can start to identify angles. We already know that side C is 90°. Lets start finding side B. I have identified all the sides with B as the reference angle. I will use Tan to find B.

TanB=29/38

B=Tan-129/38

B=Tan-10.76

B=37°

How we can solve for A.

180-90-37=53

Here is the solved triangle.

Math 10

Week 3 – math 10 – Trigonometric ratios

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This week in math we started to learn about trigonometry, the study of triangles. The base of trigonometry are the trigonometric ratios: Sine, Cosine, and Tangent. But in order to understand equations, you need to understand triangles.

This is a right-angle triangle. The corner with the x in it is the reference angle and the hole equation is based around this. The longest side is they hypotenuse marked by a H. The side across from the reference angle is the opposite side, marked with the O. the final side is known as the adjacent side, marked with A, is beside the reference angle.

Here are the equations

Sine = O/Hs

Sine fined the relationship between the percentage of the opposite side to the Hypotenuse.

Cosine = A/H

Sine fined the relationship between the percentage of the adjacent side to the Hypotenuse.

Tangent = O/A

Sine fined the relationship between the percentage of the opposite side to the Adjacent side.

Below is an example of the with all of the equations

Math 10

Week 2 – Math 10 – Negative Exponents

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This week in math we learned about negative exponents and how to deal with them

Unlike with positive exponents, the bigger the exponent the larger the number. If you have a negative exponent and number will be smaller than 1.

24 = 16

23 = 8

22 = 4

21 = 2

20 = 1

2-1 = \frac{1}{-2}

2-2 = \frac{1}{-4}

2-3 = $latex \frac{1}{-8}

To solve for a negative fraction, we need to find the reciprocal fraction. For example \frac{2}{1} is the reciprocal of \frac{1}{2}. When we reciprocate a negative exponent, the exponent because positive and the question becomes easier to solve. Reminder, when you reciprocate, it only applies to the exponent, so a positive 4 will not become negative if you reciprocate it.

3-2

Reciprocate

\frac{1}{3^2} = \frac{1}{9}

A good way to remember this is too think about wanting to make the exponents happy. If a exponent is negative, or unhappy, move it to where it will be positive, or happy.

Math 10

Week 1 – Math 10 – Prime Factors

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This week we learned about Prime Factoring. Prime Factoring is taking a number and finding its Prime Factors. For example the prime factorization of 12 is 22 x 3 or rewritten is 2 x 2 x 3.

In order to find a number’s prime factors, you need to follow divisibility rules.

2 – ends in an even number

3 – add all digits. If the sum is divisible by 3, the number is divisible by 3

4 – the last 2 digits of a number are divisible by 4. Can be cut in half twice

5 – ends in a 5 or 0

6 – if both 2 and 3 apply

7 – there is no rule

8 – can be cut in half 3 times

9 – digit sum is divisible by 9

10 – ends in a 0

Here is a guide to factorization:

  1. Check if your number is divisible by 2 (if there is any larger number that is divisible do that)
    1. If yes move on to the next step
    2. If no skip to step 4
  2. Divide
  3. Check if your quotient is still divisible by 2
    1. If yes, go back to step 2
    2. If no, move on the next step
  4. Repeat step 1-3 for the other factorization numbers