Polynomials and Polynomial Functions

Question 1

What is degree, and define its importance.

Answer 1

The degree of a polynomial function is the greatest degree among the monomial terms, and it gives information about end behavior, turning points, and the # of solutiosn that are being dealt with.

Question 2

What do you know if the degree is odd? If the degree is even?

Answer 2

odd degree:

• even # of turning points
• if a > 0, the line starts in the bottom left and ends in the top right
• if a < 0, the line starts in the bottom right and ends in the top left

even degree:

• odd number of turning points
• if a > 0, both ends will be pointing up (parabola)
• if a < 0, both ends will be pointing down (parabola)

Question 3

Define multiplicity.

Answer 3

The ______ of a zero of a polynomial function is the number of times the related linear factor is repeated in the factored form of the polynomial.

Question 4

Point of Tangency

Answer 4

This is another term for a point that is the zero of an even multiplicity; this is the point where the “bounce” occurs.

Question 5

Point of Inflection

Answer 5

This is the point that is the root of an odd multiplicity; this is the point where the “wiggle” occurs.

Question 6

How to write answer of polynomial zeros and factors:

Answer 6

For polynomials, zeros should not be given in ordered pairs, and factors should not be set equal to zero. Zeros, rather, are given in brackets, and factors are written simply as terms.