Polynomial Symmetry and Exponents

This video tutorial explains how to determine the symmetry of a polynomial by examining the exponents of its terms. A polynomial is symmetric to the Y-axis if all exponents are even, symmetric to the origin if all exponents are odd, and has no symmetry if the exponents are mixed. The tutorial provides three examples to illustrate these concepts: an even polynomial, a polynomial with mixed exponents, and an odd polynomial.

What is the symmetry of a polynomial if all its exponents are even?

• No symmetry

• Symmetric to the origin

• Symmetric to the Y-axis

• Symmetric to the X-axis

In the first example, why is the constant term considered even?

• Because it has an exponent of 3

• Because it has an exponent of 2

• Because it has an exponent of 0

• Because it has an exponent of 1

What is the symmetry of a polynomial with exponents 4, 2, and 0?

• No symmetry

• Symmetric to the X-axis

• Symmetric to the Y-axis

• Symmetric to the origin

If a polynomial has mixed even and odd exponents, what is its symmetry?

• No symmetry

• Symmetric to the X-axis

• Symmetric to the Y-axis

• Symmetric to the origin

In the second example, why is the polynomial neither even nor odd?

• Because it has no exponents

• Because the exponents are mixed

• Because all exponents are odd

• Because all exponents are even

What is the symmetry of a polynomial if all its exponents are odd?

• No symmetry

• Symmetric to the X-axis

• Symmetric to the Y-axis

• Symmetric to the origin

In the third example, why is the polynomial considered odd?

• Because all exponents are even

• Because it has an even number of terms

• Because it has an odd number of terms

• Because all exponents are odd