Question

List the various methods and general factoring forms for common factorable quadratic and cubic functions.

Accepted Answer

*   Factoring greatest common factor (GCF) (example):    
$$x^4 + x^3 + x^2 = 0$$ becomes $$x^2(x^2 + x + 1) = 0$$

*   Quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$   

*   Difference of squares: $$x^2 - y^2$$ factors to $$(x + y)(x - y)$$   

*   Completing the square: $$x^2 + bx = c$$,    
add $$\frac{b}{2}^2$$ to both sides,   
left side becomes $$(x + \frac{b}{2})^2 = c + \frac{b}{2}$$

*   Difference of cubes: $$x^3 - y^3 = (x - y)(x^2 + xy + y^2)$$   

*   Sum of cubes: $$x^3 + y^3 = (x + y)(x^2 - xy + y^2)$$   

*   Factor by grouping (example):    
$$x^3 + x^2 + x + 1 = 0$$,    
group terms $$(x^3 + x^2) + (x + 1) = 0$$,    
factor from groups: $$x^2(x + 1) + 1(x + 1) = 0$$,    
factor common expression: $$(x + 1)(x^2 + 1) = 0$$

Flashcard 4 - Next Generation Advanced Algebra and Functions Flashcard Set for the ACCUPLACER Test

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