Polynomial Operations

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 like terms?

Back

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

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5x) = (2x^2 + 4x^2) + (3x + 5x) = 6x^2 + 8x.

Front

What is the degree of a polynomial?

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 subtract polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms. For example, (3x^2 + 4x) - (2x^2 + 5x) = (3x^2 - 2x^2) + (4x - 5x) = x^2 - x.

Front

What is the product of two binomials?

Back

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

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, while a polynomial can have multiple terms. For example, 3x is a monomial, while 3x + 2 is a polynomial.

Front

How do you multiply a polynomial by a monomial?

Back

To multiply a polynomial by a monomial, distribute the monomial to each term in the polynomial. For example, 3x(2x^2 + 4x) = 6x^3 + 12x^2.

Front

What is the zero product property?

Back

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero. For example, if (x - 2)(x + 3) = 0, then x - 2 = 0 or x + 3 = 0.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 4x^3 + 2x^2 - x + 5 is in standard form.