Question

Consider the polynomial f(x)=2x^5-3x^4+x-6 (x )equals 2 x Superscript 5 Baseline minus 3 x Superscript 4 Baseline plus x minus 6. Write the degree of this​ polynomial, its leading​ term, its leading​ coefficient, and its constant term.

Answer 1

The degree of the polynomial f(x)=2x^5-3x^4+x-6 is 5. The leading term is 2x^5, the leading coefficient is 2, and the constant term is -6.

Step-by-step explanation:

The degree of a polynomial is determined by the highest power of x in the polynomial. In this case, the highest power is 5, so the degree of the polynomial is 5.

The leading term of a polynomial is the term with the highest power of x. In this case, the leading term is 2x5.

The leading coefficient of a polynomial is the coefficient of the leading term. In this case, the leading coefficient is 2.

The constant term of a polynomial is the term that does not have x as a factor. In this case, the constant term is -6.

Answer 2

degree of polynomial = 5

leading term =
`2x^(5)`

leading coefficient = 2

constant term = -6

Step-by-step explanation:

`f(x) = 2x^(5)-3x^(4)+x-6`

(i) The degree of the polynomial = 5. That is, the highest power of x

(ii) Leading term =
`2x^(5)`. This is the term with the highest power of x.

(iii) Leading Coefficient = 2. That is, the coefficient of the leading term (
`2x^(5)`)

(iv) Constant term = -6. This is the term that is independent of x or the term in which x doesn't appear.