Question

Consider the following polynomial expression: ( 194652 + 8ab^3c - 27a^7 ). When asked to identify the degree of the polynomial, Alexander said the degree is 6, and Christian said the degree is 8. Who do you agree with and why?

a) Alexander; the degree is 6.
b) Christian; the degree is 8.
c) The degree is neither 6 nor 8.
d) The degree is 7.

Answer 1

The degree of the given polynomial is 7, as determined by the term -27a⁷, which has the highest power among the terms of the polynomial. Both Alexander and Christian's answers are incorrect.

Step-by-step explanation:

To determine the degree of the polynomial, we look at the highest power of the variables in any term of the polynomial. In the expression (194652 + 8ab³c - 27a⁷), the terms are 194652, 8ab³c, and -27a⁷. The first term is a constant with a degree of 0, and the second term has a degree of 4 (since b is raised to the power of 3, c to the power of 1, and the sum of the powers of the variables is 3 + 1), and the third term has a degree of 7 (since a is raised to the power of 7). Therefore, the highest degree among the terms is 7, corresponding to the term -27a⁷.

In conclusion, the degree of the polynomial is 7. This means option d) the degree is 7 is the correct answer. Hence, both Alexander and Christian are incorrect in their assessments.