Question

Among the following polynomial of degree 10 is

A) 10x2
B)x10
C) xlo
10
D) (x + 10)
​

Answer 1

Answer:

6

Step-by-step explanation:

Definition: The degree is the term with the greatest exponent

Recall that for y2, y is the base and 2 is the exponent

Example #1:

4x2 + 6x + 5

This polynomial has three terms. The first one is 4x2, the second is 6x, and the third is 5

The exponent of the first term is 2

The exponent of the second term is 1 because 6x = 6x1

The exponent of the third term is 0 because 5 = 5x0

What? 5x0 = 5?

Well, anything with an exponent of 0 is always equal to 1

Thus, 5x0 = 5 × x0 = 5 × 1 = 5

Since the highest exponent is 2, the degree of 4x2 + 6x + 5 is 2

Example #2:

2y6 + 1y5 + -3y4 + 7y3 + 9y2 + y + 6

This polynomial has seven terms. The first one is 2y2, the second is 1y5, the third is -3y4, the fourth is 7y3, the fifth is 9y2, the sixth is y, and the seventh is 6

The exponent of the first term is 6

The exponent of the second term is 5

The exponent of the third term is 4

The exponent of the fourth term is 3

The exponent of the fifth term is 2

The exponent of the sixth term is 1 because y = y1

The exponent of the last term is 0 because 6 = 6x0

Since the highest exponent is 6, the degree of 2y6 + 1y5 + -3y4 + 7y3 + 9y2 + y + 6 is 6