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)

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