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, along with 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 + 7, the degree is 3.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms. For example, (3y^2 + y^3 - 5) + (4y^2 - 4y + 2y^3 + 8) = (1y^3 + 3y^2 + 4y^2) + (-4y) + (3) = 3y^3 + 7y^2 - 4y + 3.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (3 - 2x + 2x^2) - (4x - 5 + 3x^2) = (2x^2 - 3x + 8).

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, (3r - 4)(7r - 5) = 21r^2 - 15r - 28r + 20 = 21r^2 - 43r + 20.

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 difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, such as 5x or -3y^2. A polynomial can have multiple terms, such as 2x^2 + 3x - 1.

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.

Front

How do you simplify a polynomial expression?

Back

To simplify a polynomial expression, combine like terms and eliminate any unnecessary parentheses. For example, (x^2 - 3x - 2) + (5x^2 + 10x - 5) simplifies to 6x^2 + 7x - 7.

Front

What is the zero polynomial?

Back

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