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POLYNOMIALS - Coggle Diagram

- - - - :check:For the polynomials A(x), B(x), and C(x), A(x).B(x)+A(x).C(x)=A(x).[B(x)+C(x)]
        :check: The area that corresponds to x2+ax is drawn separately and then together.
    - - a) Perfect Square:
        :star: The expressions in the form of (x+y)2 or (x+y)2 are called perfect square expressions.
      - b) Difference of Two Square:
        :star: The difference between two squares is the form of x2 + y2.
      - c) Factoring the Cube of Sum and Difference:
        :star: For the difference of cubes, the "minus" sign goes in the linear factor, a – b; for the sum of cubes, the "minus" sign goes in the quadratic factor, a2 – ab + b2.
      - d) Factoring the Sum and Difference of Two Cube:
        :star: For the “difference” case, the binomial factor on the right side of the equation has a middle sign that is negative.
        :star: In addition to the “difference” case, the middle sign of the trinomial factor will always be opposite the middle sign of the given problem. Therefore, it is positive.
      - 4-Factoring Three Terms Polynomial:
        :star: We need to find numbers a and b such that q(x) = x2 − 5x + 6 = (x − a)(x − b)
        :star: This generally involves some guessing and checking to get the right combination of numbers. The number 6 has factors 1, 2, 3, and 6 so it's very likely our a and b will be chosen from those numbers.
      - 5-Factoring by Changing the Variable:
        :star: It is the process of simplifying the polynomial by renaming similar terms with a new variable.