polynomial expressions

Question

what is the degree of the polynomial, -7x4+3x3-8x2+2x-7

Answer 1

The degree of a one-variable polynomial is equal to the highest exponent attached to that variable. For you, the highest exponent is 4 (in the term -7x⁴), so the degree is 4.

 

In a more complicated case with multiple variables, like x⁹y⁴ + 3x¹² + 14x²y³ - 10, the degree is the highest combined degree of any term. The first term has a degree of 9+4 = 13, the next term has a degree of 12, the next term has a degree of 2+3 = 5, and the last term has a degree of 0. So, this polynomial has a degree of 13.