Question

What is the degree of the polynomial f(x) = 3 - 10x + 5x⁴ + 5x² + 8x⁷?

1) 1
2) 2
3) 4
4) 7

Answer 1

The degree of the polynomial f(x) = 3 - 10x + 5x⁴ + 5x² + 8x⁷ is 7, which is the highest exponent of x in the expression.

Step-by-step explanation:

The degree of a polynomial is the highest power of the variable x that appears in the expression with a nonzero coefficient. To find the degree, you look at each term of the polynomial and identify the highest exponent. In the polynomial f(x) = 3 - 10x + 5x⁴ + 5x² + 8x⁷, we see terms with exponents of 1, 2, 4, and 7. Therefore, the highest power is 7, which makes the degree of this polynomial 7. The correct answer is option 4).