Simplify completely quantity 4 x squared minus 32 x plus 48 all over quantity 3 x squared minus 17 x minus 6.

Answer
(4x-8)(3x-1)


Explanation(4x²-32x+48)/(3x²-17x-6)
First factorize the numerator the the denominator.4x²-32x+48 = 4(x²-8x+12)Factorize x²-8x+12. product = 12 and sum = -8. The factors are -6 and -2
x²-8x+12 =x² -2x -6x +12 = x(x-2) - 6(x-2) = (x-2)(x-6)
4x²-32x+48 = 4(x-2)(x-6)For the denominator; 3x²-17x-6 product = -18 and sum = -17. the factors are: -18 and 13x²-17x-6 = 3x² +1x - 18x -6 = x(3x+1) -6(3x+1) = (3x+1)(x-6)
(4x²-32x+48)/(3x²-17x-6) = 4(x-2)(x-6)/ (3x+1)(x-6) =4(x-2)/(3x-1) or = (4x-8)(3x-1)