Rational Zero Theorem Used to factor a cubic or quartic polynomial function with a leading coefficient not equal to 1.

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Presentation transcript:

Rational Zero Theorem Used to factor a cubic or quartic polynomial function with a leading coefficient not equal to 1.

Factor 3x 3 + 2x 2 – 7x + 2 We are going to need a strategy to get through the factoring… Common Factoring… Grouping…. Hope for a trinomial?.quadratic form… Factor theorem… RZT….

Factor 3x 3 + 2x 2 – 7x + 2 Let p be all the factors of the constant term: +1, -1, +2, -2 Let q be all the factors of the Lead Coefficient +1, -1, +3, -3 The possible values of are: There are some repeated values in the list…

Try 1 3(1) 3 + 2(1) 2 – 7(1) + 2 = – = 5 – = = 0 It works!!! So, (x – 1) is a factor

Try -2 3(-2) 3 + 2(-2) 2 – 7(-2) + 2 = = = = 0 It works!!! So, (x + 2) is a factor

Try 1/3 3(1/3) 3 + 2(1/3) 2 – 7(1/3) + 2 = 1/9 + 2/9 – 7/3 + 2 = 1/9 + 2/9 – 21/9 + 18/9 = -18/9 + 18/9 = 0 It works!!! So, (x – 1/3) is a factor Also written as (3x – 1)

Pg 101 (4,6,7,11) a,c,e