Multiply. x-5/4x+8*(12x^2+32x+16)
A. (3x+2)/4(x-5)
B. (x-5)(3x+2)/4
C. (x-5)(3x+2)
D. (x-5)(12x+8)
The answer is C. (x-5)(3x+2).
To multiply, we first distribute the x-5 over the parentheses:
x-5/4x+8 * 12x^2 + 32x + 16
= (x*(12x^2+32x+16) - 5/4x+8*(12x^2+32x+16))
= (12x^3+32x^2+16x - 15x^2 - 40x - 20) / (4x+32)
Simplifying the numerator:
= 12x^3+17x^2-24x-20
Now, factoring out a common factor of (x-5):
= (x-5)(12x^2+47x+4)
We can check that this is equivalent to answer choice C by expanding (x-5)(3x+2):
= 3x^2 - 13x - 10
= 3x^2+2x-15x-10
= (3x+2)(x-5)