Final answer:
The degree of the function h(x) = 2(x−3)²(x−1)²(x+4) is 5, as it is determined by summing the exponents of its expanded form without having to multiply out the individual factors.
Step-by-step explanation:
To determine the degree of the function h(x) = 2(x−3)²(x−1)²(x+4), we need to identify the highest power of x after expanding the expression. The given function is a product of three terms in the form of (x-a)^2 and (x+b). We do not need to fully expand the expression to find the degree; we simply acknowledge that (x-a)^2 contributes a power of 2 to the degree of the polynomial, and (x+b) contributes a power of 1.
The term (x−3)² has a power of 2 and so does the term (x−1)²; adding these we get 2 + 2 = 4. The term (x+4) contributes a power of 1. So, we sum all these exponents to determine the total degree of the polynomial: 4 + 1 = 5. Therefore, the degree of h(x) is 5.