etherealize
contestada

Determine if the expression - 10c3 – c4 + 3c2 is a polynomial or not. If it is a
polynomial, state the type and degree of the polynomial.

Respuesta :

xero099

Answer:

The expression is a fourth grade trinomial.

Step-by-step explanation:

Mathematically speaking, a polynomial is an equation of the form:

[tex]y = \Sigma_{i = 0}^{n} c_{i}\cdot x^{i}[/tex] (1)

Where:

[tex]y[/tex] - Dependent variable.

[tex]x[/tex] - Independent variable.

[tex]c_{i}[/tex] - i-th Coefficient of the polynomial.

[tex]n[/tex] - Grade of the polynomial

Let [tex]y[/tex] be a fourth-grade polynomial, then the expression must be in the form:

[tex]y = c_{o} + c_{1}\cdot c +c_{2}\cdot c^{2} + c_{3}\cdot c^{3} + c_{4}\cdot c^{4}[/tex] (2)

If we know that [tex]c_{o} = c_{1} = 0[/tex], [tex]c_{2} = 3[/tex], [tex]c_{3} = -10[/tex] and [tex]c_{4} = -1[/tex], then we have the following polynomial:

[tex]y = 3\cdot c^{2}-10\cdot c^{3}-c^{4}[/tex]

By Commutative Property:

[tex]y = -10\cdot c^{3}-c^{4}+3\cdot c^{2}[/tex]

We have a polynomial with three elements.

Therefore, the expression is a fourth grade trinomial.

Following are the calculation on the polynomial equation:

Given:

[tex]-10c^3 - c^4 + 3c^2[/tex]

To find:

degree of the polynomial=?

Solution:

[tex]\to -10c^3 - c^4 + 3c^2[/tex]

In the above given polynomial expression, we use the property of the polynomial expression therefore the degrees of the polynomial is "4".

Learn more about the degree of the polynomial:

brainly.com/question/20456724

Ver imagen codiepienagoya

Otras preguntas