Adding, Subtracting, & Classifying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 3x^2 + 2x - 5 is a polynomial.

Front

What are the degrees of polynomials?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 4x^3 + 2x^2 - x, the degree is 3.

Front

How do you classify polynomials based on the number of terms?

Back

Polynomials can be classified as monomials (1 term), binomials (2 terms), or trinomials (3 terms). For example, 5x is a monomial, 3x + 2 is a binomial, and x^2 + 3x - 4 is a trinomial.

Front

What is the process of adding polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (3x^2 + 2x) + (4x^2 + 5x) = (3x^2 + 4x^2) + (2x + 5x) = 7x^2 + 7x.

Front

What is the process of subtracting polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms. For example, (5x^2 + 3) - (2x^2 + 1) = (5x^2 - 2x^2) + (3 - 1) = 3x^2 + 2.

Front

What is a binomial?

Back

A binomial is a polynomial that contains exactly two terms. For example, 3x + 4 is a binomial.

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What is a trinomial?

Back

A trinomial is a polynomial that contains exactly three terms. For example, x^2 + 5x + 6 is a trinomial.

Front

What is the difference between a linear polynomial and a quadratic polynomial?

Back

A linear polynomial has a degree of 1 (e.g., 2x + 3), while a quadratic polynomial has a degree of 2 (e.g., x^2 + 4x + 4).

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How do you identify like terms in a polynomial?

Back

Like terms are terms that have the same variable raised to the same power. For example, in the polynomial 3x^2 + 5x^2 - 2x, the terms 3x^2 and 5x^2 are like terms.

Front

What is the result of subtracting (4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1)?

Back

The result is -8n^2 - 8n + 3.