Question

which term has the highest degree in the polynomial $3x^4 - 7x^2 + x - 10$?
a. $3x^4$
b. $-10$
c. $x$
d. $-7x^2$

Explanation:

Step1: Define degree of a term

The degree of a term with a variable is the exponent of the variable. For constants, the degree is 0.

Step2: Calculate degree of each term

• For $3x^4$: degree = 4
• For $-10$: degree = 0
• For $x$: degree = 1
• For $-7x^2$: degree = 2

Step3: Compare degrees

$4 > 2 > 1 > 0$, so $3x^4$ has the highest degree.

Answer:

a. $3x^4$