Question

Determine the degree of the polynomials.
a) 7
b) 5
c) 4
d) 3

Answer 1

a) The degree of the polynomial is 0.

b) The degree of the polynomial is 1.

c) The degree of the polynomial is 2.

d) The degree of the polynomial is 3.

Step-by-step explanation:

Understanding the degree of a polynomial involves identifying the highest power of the variable within the expression. In option a), where the polynomial is a constant (7), there is no variable present. A constant term is considered a degree 0 polynomial, as it can be expressed as
`\(7 * x^0\)`, where
`\(x^0\)` is equal to 1. Thus, the degree is 0 for option a).

Moving to option b), where the polynomial is a linear expression represented by the variable x without any exponent, it is considered a degree 1 polynomial. The highest power of the variable is 1, making the degree 1.

In option c), the polynomial involves a variable raised to the power of 2 (x²). This represents a quadratic expression, and the highest power is 2, so the degree of the polynomial is 2.

Lastly, in option d), the polynomial contains a variable raised to the power of 3 (x³). This cubic expression makes the degree of the polynomial 3, as the highest power is 3.

Therefore, the degrees of the given polynomials are 0, 1, 2, and 3, respectively.

Complete Question:

Determine the degree of the following polynomials:

a)
`\(7\)`

b)
`\(5x\)`

c)
`\(4x^2\)`

d)
`\(3x^3\)`