Polynomials are math expressions joined together by operation signs, but division is not included in the terms because its illegal, however, they can be use by divided 2 polynomials by each other.

The degree of a polynomial is the highest exponent value in the polynomial.

ex: deg(2x^6y^2)=6

Standard form is when you order all terms from greatest exponential to the least(constant).

5+2x+x^2 will be x^2+2x+5

If a polynomial has like terms, sum them to simplify:

5x^2+3x+5x+7+9, like terms 3x+5x=8x, 7+9=16; 5x^2+8x+16

Types:

Monomials have 1 term, binomials have 2, trinomials have 3 and so on.

A zero polynomial has a degree equal to 0.

A constant polynomial has no variables, 3,5,6,7,etc

Linear polynomials have a degree of 1, quadratic polynomials have a degree of 2, and cubic polynomials have a degree of 3, quartic, quintic, sextic, septic...

Below is the list of theorems for polynomials. It is difficult to explain: suggestion: watch a video on youtube;

Polynomial operations:

ADDITION:

In addition, you place the terms on top of each other and sum up the like terms.

SUBTRACTION:

In subtraction, you place the terms on top of each other and subtract the like terms.

MULTIPLICATION:

(ax^n+...+bx+c)(ax^n+...+bx+c): In multiplication, you multiply the first term in the first polynomial, use the add or subtract signs in the 2nd polynomial to know, then do it for the 2nd term, and then the nth term. Then multiply the 2nd term in the first polynomial by the 1st term in the 2nd polynomial and then to the nth term and then multiply the nth term in the first polynomial by the first 2nd and nth terms of the second one. Combine like terms to simplify. And you're done!

DIVISION:

FACTORIZATION:

The factorization of a polynomial is when you simplify it to 2 smaller polynomials multiplied by each other:

Polynomial equations:

A polynomial equations is formed by exponents, variables, coefficients, constants, and a equal sign in standard form.

P(x) = an xn + . . + a1x + a0=T

Polynomials functions is when polynomials are functions:

Linear quadratic cubic...

all form curves and parabolas except for linears.

ZEROS OF POLYNOMIAL+FACTORIZATION OVERVIEW:

p(α) = 0 and p(ß) = 0 meaning if x=α or ß, if (α or ß)  ±  c=0, therefore, (α or ß)  ±  c is a factor of p(x)