What I Have Learned About Grade 9 Polynomials.

In this term, we have learned about polynomials and how to add, subtract, multiply and divide them.

Definitions:

Term: An expression formed from the product of numbers and/or variables. An example of an expression with 3 terms would be $5xy^2$ + 3x – 5. This example would be called a Trinomial because it is a expression that consists of three terms. The terms can be separated by addition, subtraction, multiplication or division.
Coefficient: When a term consists of a number before a variable, the number is thought of as a coefficient. An example would be 6z which means 6 times z, and “z” is a variable, so 6 is a coefficient.
Constant: A number on its own would be a constant. In the expression 4x-7 = 5, the numbers 5 &7 would be constants because they are on their own, without and exponents or variables after them.
Degree of a Term: The sum of the exponents on the variables in a single term (monomial). An example of the degree of a monomial would be $2b^3$ The degree would be 3.
Degree of a Polynomial: The degree of the highest-degree term in a polynomial. In the example $7a^2$ -3a the degree of the first term is 2 and the degree of the second term is 1, so the highest degree is 2, so the degree of the polynomial is 2.

When you are adding and subtracting polynomials without brackets, all you have to do is group and simplify.
Once you have the question, the first thing you need to do is to group your like terms together (Like terms are terms that all consist of the same variables and exponents. Unlike terms are terms that do not).
Your second step is to add or subtract your like terms together. You may not add or subtract unlike terms.
At the end, you have finished the question with a simplified form.
Note: Always group & simplify the terms from biggest to smallest.

Adding Polynomials with brackets is similar to adding without.
When there is an addition sign between to bracketed polynomial questions, all you have to do is take away the brackets & addition sign and simplify the question.

When you see a subtraction sign in front of a bracketed polynomial question, you change the numbers to their opposite. So if the numbers in the brackets were originally (-4 +5), you would change it to (+4 -5).
Then, you take the brackets away and simplify the question.

Multiplying is just like finding the area of a rectangle.
When you multiply polynomials, you need to remember to multiply the coefficient, keep the variable and just like in our exponent unit, add the exponents together. Example: $2x\cdot2x$ = $4x^2$ (because there is an invisible 1 for the exponent of the x).
Note: That if the variables are different, you can not add them together.

Dividing Polynomials is just like multiplying, instead you divide the coefficient and subtract the exponents. Example: $24x^3\div6x$ = $4x^2$
Note: If the variables are different, you can not subtract them.

Let’s say that you have a question like 3x(6+4x). In this case you would use the distribution method.
You multiply the term on the outside of the brackets with each term on the inside of the brackets.

Example: 3x(6+4x)

(3x)(6) (3x)(4x)

18x + $12^2$