Question 1204305
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Determine whether the binomial (3x-2) is a factor of the polynomial {{{3x^3-14x^2+26x-12}}}.
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Alternatively to other methods, you can factor the polynomial explicitly, 
using the grouping and re-grouping method and applying it step by step.


This is made easier by the fact that the basic binomial 3x-2 is just given to work with it.



3x^3 - 14x^2 + 26x - 12 = group and re-group the terms step by step = (3x^2 - 2x^2) - 12x^2 + 26x - 12 = 

= x^2*(3x-2) - (12x^2 -26x) - 12 = x^2*(3x-2) - (12x^2 - 8x) - 8x + 26x - 12 = x^2*(3x-2) - 4x(3x-2) + (18x-12) = 

= x^2*(3x-2) - 4x(3x-2) + 6(3x-2) = take off the common factor (3x-2) = (3x-2)*(x^2 - 4x + 6).


The last formula shows explicitly that (3x-2) is the factor.
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Solved.