Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 3x² - 2x + 5 is a polynomial.

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 4x³ + 2x² - x, the degree is 3.

Front

How do you add polynomials?

Back

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

Front

How do you subtract polynomials?

Back

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

Front

What is a like term?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x² and 5x² are like terms.

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, 4x³ + 2x² - x is in standard form.

Front

How do you multiply a polynomial by a monomial?

Back

To multiply a polynomial by a monomial, distribute the monomial to each term of the polynomial. For example, 2x(3x + 4) = 6x² + 8x.

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. For example, (x + 2)(x + 3) = x² + 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, and 3x + 2 is a polynomial.

Front

What is the zero polynomial?

Back

The zero polynomial is a polynomial that has no terms and is equal to zero. It is represented as 0.