A polynomial function with real coefficients has real zeros. This is sometimes true because say we have an equation x^2+10. If you graph this, you will notice that there are no points on the x axis, or no zeroes. x^2+10 is a real number equation without any complex numbers so the answer is sometimes true.

## What is a polynomial with real coefficients?

A polynomial having only real numbers as coefficients. A polynomial with real coefficients is a product of irreducible polynomials of first and second degrees. SEE ALSO: Polynomial.

## Can a degree 6 polynomial with real coefficients have exactly 0 real roots?

A polynomial can’t have more roots than the degree. So, a sixth degree polynomial, has at most 6 distinct real roots.

## How do you find the leading coefficient of a polynomial function?

How To: Given a polynomial expression, identify the degree and leading coefficient.

1. Find the highest power of x to determine the degree.
2. Identify the term containing the highest power of x to find the leading term.
3. Identify the coefficient of the leading term.

## What is the leading term of the polynomial function?

Printable version. In a polynomial, the leading term is the term with the highest power of x. For example, the leading term of 7+x−3×2 is −3×2. The leading coefficient of a polynomial is the coefficient of the leading term.

## How did you determine the degree of the polynomial?

In the case of a polynomial with more than one variable, the degree is found by looking at each monomial within the polynomial, adding together all the exponents within a monomial, and choosing the largest sum of exponents. That sum is the degree of the polynomial.

## How do you know if a polynomial is odd or even?

for all x in the domain of f(x), or odd if, f(−x) = −x, for all x in the domain of f(x), or neither even nor odd if neither of the above are true statements. A kth degree polynomial, p(x), is said to have even degree if k is an even number and odd degree if k is an odd number.

## How do you tell if a polynomial is odd or even?

In general, we can determine whether a polynomial is even, odd, or neither by examining each individual term. A polynomial is even if each term is an even function. A polynomial is odd if each term is an odd function. A polynomial is neither even nor odd if it is made up of both even and odd functions.

## How do you know if its a polynomial function?

In particular, for an expression to be a polynomial term, it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions.