Find the Degree f(x)=2x^2(x-1)(x+2)^3(x^2+1)^2

Problem

ƒ(x)=2*x2*(x−1)*(x+2)3*(x2+1)2

Solution

1. Identify the degree of each individual factor in the polynomial expression.

2. Determine the degree of the first factor 2*x2 which is 2

3. Determine the degree of the second factor (x−1) which is 1

4. Determine the degree of the third factor (x+2)3 by multiplying the internal degree by the exponent: 1×3=3

5. Determine the degree of the fourth factor (x2+1)2 by multiplying the internal degree by the exponent: 2×2=4

6. Sum the degrees of all factors to find the total degree of the polynomial ƒ(x)

2+1+3+4=10

Final Answer

Degree*(ƒ(x))=10

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