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The degree is the highest power of the variable. For example, x5 + 3x3 - x + 4 is of degree 5, since the highest power of "x" is 5.

Q: What is a degree of a real polynomial?

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The polynomial 7x3 + 6x2 - 2 has a degree of 3, making it cubic.

Factors

Yes, f(x) = 2 is a polynomial of degree 0 (because there are no x terms).

A binomial.

quadratic

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A third degree polynomial could have one or three real roots.

Sort of... but not entirely. Assuming the polynomial's coefficients are real, the polynomial either has as many real roots as its degree, or an even number less. Thus, a polynomial of degree 4 can have 4, 2, or 0 real roots; while a polynomial of degree 5 has either 5, 3, or 1 real roots. So, polynomial of odd degree (with real coefficients) will always have at least one real root. For a polynomial of even degree, this is not guaranteed. (In case you are interested about the reason for the rule stated above: this is related to the fact that any complex roots in such a polynomial occur in conjugate pairs; for example: if 5 + 2i is a root, then 5 - 2i is also a root.)

seventh degree polynomial x3 times x4 = x7

It depends on the polynomial and your degree of sophistication. In the complex domain, it will have six solutions, although not all of them need be different. If the coefficients are all real, then it will have 0, 2, 4 or 6 real solutions in the real domain.

If the domain is infinite, any polynomial of odd degree has infinite range whereas a polynomial of even degree has a semi-infinite range. Semi-infinite means that either the range has a real minimum but no maximum (ie maximum = +infinity) or that it has a real maximum but no minimum (ie minimum = -infinity).

No. A quadratic polynomial is degree 2 (2 is the highest power); a cubic polynomial is degree 3 (3 is the highest power).No. A quadratic polynomial is degree 2 (2 is the highest power); a cubic polynomial is degree 3 (3 is the highest power).No. A quadratic polynomial is degree 2 (2 is the highest power); a cubic polynomial is degree 3 (3 is the highest power).No. A quadratic polynomial is degree 2 (2 is the highest power); a cubic polynomial is degree 3 (3 is the highest power).

A fourth degree polynomial.

The degree of a polynomial is the highest power of the variable.

The degree of the polynomial.

a polynomial of degree...............is called a cubic polynomial

A polynomial of degree 0 is a polynomial without any variables, such as 9.

The degree of a polynomial is the highest exponent on any independent variable in the polynomial.