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POLYNOMIALS - Coggle Diagram

- - - - x - 3 is the dividend polynomial
        
        2x^2 + x - 5 is the quotient polynomial.
        
        2x^3 - 5x^2 - 8x + 15 is the divisor polynomial
        
        0 is the remainder polynomial
- - - - The highest power in a polynomial is called degree of polynomial and it is shown as d[p(x)] or deg[p(x)]
    - - The term with the degree 0 is called the constant term
        
        In order to find the constant term of a polynomial we substitute zero for each variable.
    - - The term with the largest degree is called leading coefficent
    - - The number that is being multiplied by the variable is called the coefficients
    - - In order to find the sum of the coefficients of a
        polynomial we substitute 1 for each variable
- - - - This process is done by factoring out the common factor
        
        For the polynomials A(x), B(x), and C(x),
        A(x).B(x) + A(x).C(x) = A(x).[B(x) + C(x)]
    - - Perfect Square
        
        The expressions in the form of (x + y)^2 and (x - y)^2 are called perfect squares
      - Difference of Two Square
        
        it is a form of x^2 - y^2 = (x - y) (x + y)
      - Factoring the Cube of Sum and Difference
        
        (x + y)^3 = x^3 + 3yx^2 + 3xy^2 + y^3 --> x^3 + y^3 = (x + y)^3 - 3xy(x + y)
        
        (x - y)^3 = x^3 - 3yx^2 - 3xy^2 - y^3 --> x^3 - y^3 = (x - y)^3 + 3xy(x - y)
      - Factoring the Sum and Difference of Two Cube
        
        x^3 + y^3 = (x + y) (x^2 - xy + y^2)
        
        x^3 - y^3 = (x - y) (x^2 + xy + y^2)
    - - If there is no common term in every term of the polynomials, the terms that have any common factors are form a group by coming together. Now that they have the same expression in parentheses, we can factor out these groups.
    - - In this method we simplify the polynomial by renaming similar terms with new veriables