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The polynomial p(x) = 3x^3 - 20x^2+ kx + 12 is divisible by x - 3 for some constant k. Factor p(x) completely.

 Feb 15, 2021
 #1
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Using long division, divide (x-3) into funtion  p

 

                        3x^2 -11x -4

 x-3 |    3x^3 - 20x^2+ kx + 12

            3x^3 - 9x^2

                      -11x^2 + kx

                      -11x^2  + 33x               k will need to be 29 for this to work out without a remainder

                                  -4x + 12

                                  -4x +12

                                             0

 

so we have one root    x-3   

             now we need to factor    3x^2-11x-4 

                                 (x-4)(3x+1)        (I used the quadrtatic formula here......but some folks can just 'see' the factors....(CPhill)  )

 

so p factored =   (x-3)(x-4)(3x+1)

 

 Feb 15, 2021

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