What I have learned about grade 9 polynomials

What is a polynomial?

a polynomial is a math expression or question that consists of coefficients and variables.

There are 3 types of polynomials a monomial, a binomial and a trinomial.

monomial ex: $5x$

(has 1 term)

binomial ex: $5x\cdot7x^2$

(has 2 terms)

trinomial ex: $5x\cdot7x^2-4$

(has 3 terms)

You can tell easily what type of polynomial it is by looking at the terms.

What is a term?

a term is each little part in the expression.

ex: $12$

ex: $3x^2$

ex: $-5x^3$

in this next expression im going to add the terms together to make an expretion with 3 terms.

$12+3x^2-5x^3$

(Anything with more then 3 terms is considered a polynomial.)

Degree of a term or polynomial

what is a degree? you may ask.

well the degree of a term is the amount of variable exponents in the term added up.

ex: $2x^4$

in this example the degree is 4 because the variable has an exponent of 4 which means.

$x\cdot x\cdot x\cdot x\cdot 2$

and that expression has 4 variables.

this expression: $12x$ has a degree of 1 because the $x$ has a secret exponent of 1 $x=x^1$

(anything that isn’t a variable doesn’t change anything.)

How to add polynomials

Polynomials are pretty cool and easy to work with. To add them it’s very simple, you just stick them together to make a bigger polynomial. Whoa!!!

ex: $(6x^2+4x-1)+(-x^2+2x+3)$ =

$6x^2+4x-1-x^2+2x+3$

after that you simplify the new and improved polynomial into the final answer.

$5x^2+6x+2$

How to subtract polynomials

subtracting polynomials is easy. there are two way to subtract polynomials

there is way one were you just put them together because there is no brackets.

$x^2-6x+2$ and $2x^2+3x-3$ = $x^2-6x+2-2x^2+3x-3$

(which is then simplified like this) = $-x^2-3x-1$

and then there’s the second way where there is brackets on the fraction you are subtracting like this.

$x^2-6x+2-(2x^2+3x-3)$

for this one you need to flip everything in the brackets from positive to negative and negative to positive like this.

$x^2-6x+2-2x^2-3x+3$

then you simplify

$-x^2-9x+5$

How to multiply polynomials

There are 3 ways to multiply polynomials the first way is with no brackets. Pretty strait forward you just put them together and use BEDMAS

$-x^2-3x+4$ and $3x^2+2x-2$ =

$-x^2-3x+4\cdot 3x^2+2x-2$ =

$11x^2-x-2$

way two is with one of the polynomials in brackets. (doesn’t matter which one)

so what you do is you multiply the number outside of the brackets with each of the numbers inside the brackets.

$4+5x(3x-2x^2)$ =

$4+5x\cdot 3x+5x\cdot -2x^2$ =

$-10x^3+15x^2+4$

Way three is where there is brackets on both of the polynomials. for this you need to multiply each number in the first bracket to all the numbers in the other brackets and you need to do that with all the numbers in the first bracket.

$(x+4)(2x^3-5x+2)$

$x\cdot 2x^3+x\cdot -5x+x\cdot 2+4\cdot 2x^3+4\cdot -5x+4\cdot 2$

Then you use BEDMAS to simplify the equation

$2x^4+8x^3-5x^2-18x+8$

How to divide Polynomials

To divide polynomials it’s simple each part of the top gets divided by all of the numbers at the bottom. and if you’re dividing a $11x^2$ by $11x$ then the top exponent get subtracted by the bottom exponent and the rest is just simple division making this $x$ (Subtracting the variables only works if the bases is the same.) Other then that its just simple division.

ex: $\frac{10x-5x^2+20x^3}{5x}$ =

$2-x+4$ =

$6-x$

ex 2: $\frac{10x}{2}$ =

$5x$

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