Problem:
When x5,x+x1​ and 1+x2​+x23​ are multiplied, the product is a polynomial of degree
Answer Choices:
A. 2
B. 3
C. 6
D. 7
E. 8
Solution:
By definition, a polynomial (in x) is an expression of the form an​xn+ an−1​xn−1+⋯+a0​, where the a 's are constants and anâ€‹î€ =0. The degree is defined to be n, the highest power of x. Since
x5(x+x1​)(1+x2​+x23​)=x2(x2+1)(x2+2x+3)
one sees without actually multiplying further (if one adds the degrees of the factors on the right) that the product is a polynomial and has degree 6.