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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Factoring Polynomials

• To factor a polynomial means to write it as a product of other polynomials.
• A polynomial is prime if it cannot be written as a product of other polynomials.
• A polynomial is factored completely if it is written as a product of prime factors.

• First rule of factoring : use the distributive property to factor out the greatest common factor
• examples : • Special factorization formulas
• Square of a binomial a2 +2ab+ b2 = (a + b)2
• Square of a binomial a2 − 2ab+ b2 = (a −b) 2
• Difference of squares a2 − b2 = ( a +b)( a − b)
• Sum of cubes a3 + b3 = (a +b)( a2 −ab + b2 )
• Difference of cubes a3 − b3 = (a − b)(a2 + ab +b2 )

• examples :

4x2 − 64y2

8a3 + b3

4a2 −12ab+9b2

• Use trial and error (reverse the FOIL process) to factor trinomials of the form ax2 + bx + c
• examples :

x2 − 6x + 8

2x2 − x − 6

12x2 −11x − 5

• Four terms - try factor by grouping
• example : • examples :

8x3 + 2x −12x2 − 3

x3 − x2 − 4x + 4

• Be sure to factor each polynomial completely.
• examples :

12x2 − 22x + 6

27a4b − 8ab4