Please enable JavaScript.

Coggle requires JavaScript to display documents.

Strategies For Factoring, GCF, José Manuel Ramos / Paulo Miranda - Coggle…

- - - - Sum or difference
      - Both terms are perfect cubes
      - 2 terms
    - - First you need the cube root of the numbers and put them in a parentesis, then the first number you need to square it and then you multiply your first numbers the ones you have in a parentesis and change the sign because you will pass it to the center of the result, then you need to square the second digit in the parentesis and that's the result.
    - - x3 + 8 = (x + 2) (x2 - 2x + 4)
      - 64w3 - 125 = (4w - 5) (16w2 + 20w + 25)
  - - - In x2 you have the squared root of each term an it gives you x, and for the other number you do the squared root of it for example 25 is 5.
    - - x2 - 25
        
        (x - 5) (x + 5)
      - 12x2 - 75
        
        GCF 3 (4x2 - 25)
        
        (2x + 5) (2x - 5)
    - - It has 2 terms, and you need take the squared root of each term.
      - Difference
      - Two terms, each term is a perfect square
- - - - Make greatest common factor. Then look for the binomial in common. In a parenthesis, put the common binomial and in the other the GCF terms.
    - - m3 - m2 + 2m - 2
        
        m2 (m - 1) + 2 (m - 1)
        
        (m - 1) (m2 + 2)
      - 12a3 - 9a2 + 4a - 3
        
        3a2 (4a - 3) + 1 (4a - 3)
        
        (4a - 3) (3a2 + 1)
    - - GCF
      - Common binomials
- - - - Trinomial a ≠
    - - If possible, you have to apply the GCF. Then you need two numbers that when they are multiplicated they are the same as the first and third term product, and when they are summed or rested they are the same as the term in the middle. When you get this both numers you have to put the variable next to each other. After that, you pass down the first and third term. Finally you apply the grouping method to the first term, to the first number given, to the second number given and to the third term.
    - - 2x2 - 3x -2
        
        2x2 - 4x + x - 2
        
        2x (x - 2) + 1 (x - 2)
        
        (x - 2) (2x + 1)
      - 8x2 - 4x - 24
        
        4 ( 2x2 - x - 6)
        
        4 ( 2x2 - 4x + 3x - 6)
        
        2x ( x - 2) 3 ( x - 2)
        
        4 (2x + 3) (x - 2)
  - - - First you need to find TWO numbers that can replace the digit from the center that added or substracted give you the same, and the same two numbers multiplied need to give you the last digit, when you have those digits (4), you separe them 2 and 2 and need to find the common digits and divide them, then the result of the numbers you divide and the two numbers you are dividing with you put them in a parentesis and thats your result.
    - - x2 + 5x + 6 = x2 + 3x + 2x + 6 = (x + 3) (x + 2)
      - 2x2 - 5x - 3 = 2x2 - 6 + 1x - 3 = 2x (x - 3) 1 (x - 3) = (2x + 1) (x + 2)
    - - Trinomial
      - 2nd term has the same letter but with half of the exponent
      - Coefficient of x2 is 1
      - The third term is a number in most of the cases
  - - - You need to take the squared root of the first term, then the squared root of the last term and put it on a parentesis, then you multiply the first to the 2nd term and then always multiply for 2.
    - - m2 + 10m + 25 = (5a + 6)2
      - 36s2 - 24s + 4 = (6s - 2)2
    - - The middle term is twice the square roots of 1st and 3rd term
      - The third term is always positive
      - 1st and 3rd terms are perfect squares