Chapter 7 Polynomials

Question 1

What is a polynomial in x?

Answer 1

A polynomial in x has terms in positive integer powers of x and may also have a constant term.

Question 2

What determines the behavior of a polynomial of order n for large positive values?

Answer 2

The behavior of the curve of a polynomial of order n depends on whether n is even or odd, and whether the coefficient of the leading term is positive or negative.

Question 3

What is the maximum number of turning points in a polynomial function of order n?

Answer 3

The curve of a polynomial function of order n has up to (n - 1) turning points.

Question 4

What does the factor theorem state?

Answer 4

The factor theorem states that if (x - a) is a factor of a polynomial f(x), then f(a) = 0 and a is a root of the equation f(x) = 0.

Question 5

What is the order of a polynomial?

Answer 5

The order of a polynomial in x is the highest power of x which appears in the polynomial.