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, 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

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degrees of its terms. For example, 5x^4 - 3x^3 + 2x - 1 is in standard form.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms (terms with the same variable and exponent). For example, (3x^2 + 2x) + (4x^2 + 5) = 7x^2 + 2x + 5.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 - 3) - (2x^2 + 4) = 3x^2 - 7.

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, (a + b)(c + d) = ac + ad + bc + bd.

Front

What is the square of a binomial?

Back

The square of a binomial (a + b)^2 is calculated as a^2 + 2ab + b^2. For example, (2x + 3)^2 = 4x^2 + 12x + 9.

Front

What is the difference of squares?

Back

The difference of squares is a special product that states a^2 - b^2 = (a - b)(a + b). For example, 9 - 4 = (3 - 2)(3 + 2).

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, 3x(2x^2 + 4x) = 6x^3 + 12x^2.

Front

What is the remainder theorem?

Back

The remainder theorem states that the remainder of the division of a polynomial f(x) by (x - c) is equal to f(c).