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 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)