Question

list the degree of the given polynomial, its coefficients, and its constant term.
$6.4x^4 - 6x^3 + 5x^2 - 5x + 6.5$
what is the degree of the the given polynomial?
the degree is 4

Explanation:

Step1: Identify the highest power of x

In the polynomial \(6.4x^{4}-6x^{3}+5x^{2}-5x + 6.5\), we look at the exponents of \(x\) in each term. The exponents are 4, 3, 2, 1, and 0 (for the constant term 6.5).

Step2: Determine the degree

The degree of a polynomial is the highest power (exponent) of the variable. Here, the highest exponent is 4.

Answer:

The degree of the polynomial \(6.4x^{4}-6x^{3}+5x^{2}-5x + 6.5\) is 4.

Coefficients:

• Coefficient of \(x^{4}\): \(6.4\)
• Coefficient of \(x^{3}\): \(- 6\)
• Coefficient of \(x^{2}\): \(5\)
• Coefficient of \(x\): \(-5\)

Constant term:

The constant term is \(6.5\) (the term without a variable, which is the term with \(x^{0}\) since \(x^{0}=1\) and \(6.5\times x^{0}=6.5\)).