Question

Classify the following polynomials by the highest power of each of its terms. Combine any like terms first.

-x^2 + x - x^2 + 1
x^2 + x + 2x^3 - x
4x + x + x - 2
3x^2 + 4 - 3x^2 - 1

Answer 1

After combining like terms, the polynomials are classified by their highest powers: the first is quadratic, the second is cubic, the third is linear, and the fourth is constant.

Step-by-step explanation:

We will classify the given polynomials after simplifying them by combining like terms and noting the highest power of each term.

• -x^2 + x - x^2 + 1: Combining like terms, we get -2x^2 + x + 1. This polynomial is quadratic because the highest power of x is 2.
• x^2 + x + 2x^3 - x: Simplifying, we have 2x^3 + x^2. This polynomial is cubic because the highest power of x is 3.
• 4x + x + x - 2: After combining like terms, the expression simplifies to 6x - 2, which is a linear polynomial since the highest power of x is 1.
• 3x^2 + 4 - 3x^2 - 1: Combining like terms gives us 3. This is a constant polynomial because it does not contain any variables.