Question

question 3 of 10
enter the degree of the polynomial below.
$7x^7 + 10x^4 + 4x^3 - 5x^{11} - 10x^6 - 6x^7$

a. 10
b. 7
c. 11
d. 6

Explanation:

Step1: Simplify the Polynomial

First, combine like terms. The terms with \(x^7\) are \(7x^7\) and \(-6x^7\). Combining them: \(7x^7 - 6x^7 = x^7\). So the polynomial becomes \(x^7 + 10x^4 + 4x^3 - 5x^{11} - 10x^6\).

Step2: Identify the Highest Exponent

The degree of a polynomial is the highest power (exponent) of the variable in the polynomial. Looking at the simplified polynomial, the exponents are 7 (from \(x^7\)), 4 (from \(10x^4\)), 3 (from \(4x^3\)), 11 (from \(-5x^{11}\)), and 6 (from \(-10x^6\)). The highest exponent among these is 11.

Answer:

C. 11