Adding/Subtracting/Multiplying Polynomials Flashcard

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, 2x^2 + 3x - 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 4x^3 + 2x^2 - x + 7, the degree is 3.

Front

How do you add polynomials?

Back

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

Front

What are like terms?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms, while 3x^2 and 4x are not.

Front

What is the result of subtracting polynomials?

Back

To subtract polynomials, subtract the coefficients of like terms. For example, (5x^2 + 3x) - (2x^2 + x) = (5x^2 - 2x^2) + (3x - x) = 3x^2 + 2x.

Front

What is the product of two binomials?

Back

The product of two binomials can be found using the distributive property (FOIL method). For example, (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6.

Front

What is a binomial?

Back

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

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms. For example, x^2 + 3x + 2 is a trinomial.

Front

How do you classify polynomials by degree?

Back

Polynomials can be classified by degree: 0 (constant), 1 (linear), 2 (quadratic), 3 (cubic), 4 (quartic), etc.

Front

What is the sum of (3 - 2x + 2x^2) + (4x - 5 + 3x^2)?

Back

The sum is 5x^2 + 2x - 2.