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Use the polynomial 3x2−4x11+4x4−2x10−5+8x8 to answer the question. What is the degree of this polynomial?

Respuesta :

If the numbers after x are exponents(power) the the answer would be 8 has the degree but if the numbers are not raising to the power then I'm not quite sure.

carlosego

For this case we have a polynomial P (x) of the form:

[tex]P(x)=ax^n+...+bx^i+...+cx^3+dx^2+ex+f[/tex]

Where:

  • a, b, c, d, e and f: They are the coefficients of the terms of the polynomial
  • x: It is the variable associated with the polynomial
  • n, i, 3,2,1 and 0: Are the exponents. Where n is the greatest exponent.

In this way, we can say that the degree of the polynomial P (x) is n.

Then, given:

[tex]Q(x)=3x^2-4x^{11}+4x^4-2x^{10}-5+8x^8[/tex]

We order the polynomial from highest to lowest exponent:

[tex]Q(x)=-4x^{11}-2x^{10}+8x^8+4x^4+3x^2-5[/tex]

In this way, it can be seen that the largest exponent is 11.

Thus, the degree of the polynomial [tex]Q(x)=3x^2-4x^{11}+4x^4-2x^{10}-5+8x^8[/tex] is 11.

Answer:

The degree of the polynomial is 11.

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