Final answer:
The LCM of the polynomials x²+6x-16, x²-10x+16, and x²-64 is the product of their factored forms, resulting in (x+8)(x-8)(x-2).
Step-by-step explanation:
The student is asking for the least common multiple (LCM) or least common denominator (LCD) of the polynomials x²+6x-16, x²-10x+16, and x²-64. To find the LCM, we should first factor each polynomial completely.
The first polynomial factors into (x+8)(x-2), the second polynomial factors into (x-2)(x-8), and the third polynomial is a difference of squares and factors into (x+8)(x-8). The LCM of these polynomials is the product of the highest powers of all the factors that appear in any of the polynomials. Therefore, the LCM of the given polynomials is (x+8)(x-2)(x-8) which simplifies to (x+8)(x-8)(x-2).