) Identify the degree, coefficients, terms, and constant in: 6x^4 - 3x^2 + x - 8

Answer 1

In the polynomial \(6x^4 - 3x^2 + x - 8\):

1. Degree: The degree of a polynomial is the highest power of the variable \(x\) in the expression. In this case, the highest power is \(4\) (from the term \(6x^4\)), so the degree is \(4\).

2. Coefficients: The coefficients are the numerical factors in front of the variable terms. In the polynomial \(6x^4 - 3x^2 + x - 8\):

   • The coefficient of \(6x^4\) is \(6\),
   • The coefficient of \(-3x^2\) is \(-3\),
   • The coefficient of \(x\) is \(1\) (since \(x\) can be written as \(1x\)),
   • The constant term is \(-8\) (the term without \(x\)).

3. Terms: The terms of the polynomial are the individual parts of the polynomial divided by the addition/subtraction signs. The terms are:

   • \(6x^4\)
   • \(-3x^2\)
   • \(x\)
   • \(-8\)

4. Constant: The constant in the polynomial is the term that does not contain any variable \(x\). In this case, the constant is \(-8\).

To summarize:

• Degree: 4
• Coefficients: 6, -3, 1
• Terms: \(6x^4\), \(-3x^2\), \(x\), \(-8\)
• Constant: -8