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 1
3x²-17x-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)
