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GCF, Cristobal Franco and Juan Pablo Navarro, Factoring Strategies -…

- - - - Formula: The first multyply the third and then you need to look two numbers tha sum give you the second term and multyliying the first result. Then you only have to agroup.
        
        Examples:
        
        2x²-3x-2 ac=2(2)=4
        2x²-4x+1x-2
        2x(x-2)+(x-2) (x-2)(2x+1)
        
        3m²-8m-3 ac=3(3)=9 3m²-1m+9m-3
        m(3m-1)3(3m-1) (3m+1)(m-3)
  - - - Formula: a²+2ab+b² = ( a+b )² a²-2ab-b² = ( a+b ) ²
        
        Examples:
        
        x²-16x+64=(x-8)²
        
        m²+10m+25=(m+5)²
  - - - Formula: you need to find two numbers that if you sum the it give you the second term and multiply it give you the third one. Then you only have to agroup.
        
        Examples:
        
        x²+5x+6=(x+3)(x+2)
        
        x²-19x+48=(x-16)(x-3)
- - - - Formula: x² - y² = ( x + y )( x - y )
        
        Examples
        
        x²-64=(x+8)(x-8) 100x²-9=(10x+3)(10x-3)
  - - - Formulas: a³+b³=(a+b)(a²-ab+b²)
        a³-b³=(a-b)(a²+ab+b²)
        
        Examples
        
        8x³+1=(2x+1)(4x²-2x+1)
        
        27x⁴+8x⁷= x⁴(27+8x³)=x⁴(3+2x)(9-6x+4x²)
- - - - Characteristics: Have four parenthesis 2 of them are equal the other two are different.
        
        Formula: You agroup in pairs take out the GCF of the two pairs and put the result in the parenthesis.
        
        Examples:
        
        3n³-4n²+9n-12= 3n³+9n-4n²-12 = 3n(n²+3) -4(n²+3)
        
        35xy-5x-56y+8= 5x(7y-1) -8(7y-1)
    - - Characteristics: Have 4 terms 2 of them are equal and the other 2 no.
        
        Formula: You identified the equal parenthesis and then you agroup all the other terms that do not have any thing equal in another parenthesis.
        
        Examples:
        
        (a-b)(x+5)+(a-b)(x-y²)= (a-b)(2x+5-y²)
        
        (x-2)(x+5)(x-2)(x+8)= (x-2)(x+5+x+8)= (x-2)(2x+13)
    - - Formula: You agroup in pairs take out the GCF of the two pairs, if the result is equal in both you are correct then, you put the equal result in a parenthesis, and you agroup the 2 other terms in another parentheses.
        
        Examples:
        
        5pq-p²q+4p-20 = pq(5-p) +4(p-5) = -pq (-5+p)+4(p-5)= (5-p)(pq-4)
        
        3x³-6x²-x+2 = 3x²(x-2) -1(x-2) =(x-2)(3x²-1)