Question

Using remainder theorem factorize 6x 3 -25x 2 +32x - 12

Answer 1

I think it is 13 instead of 12.

P(x) = 6 x³ - 25 x² + 32 x - 13
From the coeffficeints we see that for x = 1, P(x) = 0

Hence,  (x-1) is a factor.
P(x) = (x-1) ( 6 x² - a x + 13)
        = 6 x³ - (a+6 )x² + (a+13) x- 13
comparing coefficients :   a = 19
Hence,  P(x) = (x-1) (6 x² -19 x + 13)
                     = (x -1) ( 6 x²  - 6x - 13 x + 13)
               = (x-1) (x-1) (6 x -13)