X-5/4x+8 * (12x^2+32x+16)
a- (3x+2)/2(x-5)
b- (x-5)(3x+2)/4
c- (x-5)(3x+2)
d- (x-5)(12x+8)
To find the product of X-5/4x+8 and (12x^2+32x+16), we first need to simplify X-5/4x+8.
(X-5)/(4x+8) simplifies to (X-5)/4(x+2) = (X-5)/(4(x+2)).
Now, the product of (X-5)/(4(x+2)) and (12x^2+32x+16) can be calculated as follows:
(X-5)/(4(x+2)) * (12x^2+32x+16)
= (X-5)/(4(x+2)) * 4(3x^2+8x+4)
= (X-5) * (3x^2+8x+4)
= 3x^3 + 8x^2 + 4x - 5x^2 - 8x - 4
= 3x^3 + 3x^2 - 4
Therefore, the answer is c- (x-5)(3x+2).