Adding, Subtracting and Multiplying Polynomials

Front

Define 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 is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 4x^3 + 2x^2 - x + 7, the degree is 3.

Front

What does it mean to simplify a polynomial expression?

Back

Simplifying a polynomial expression means to combine like terms and reduce the expression to its simplest form.

Front

How do you add polynomials?

Back

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

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, (5x^2 + 3) - (2x^2 + 1) = (5 - 2)x^2 + (3 - 1) = 3x^2 + 2.

Front

What is the product of two polynomials?

Back

The product of two polynomials is obtained by multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms.

Front

Multiply: (x + 2)(x + 3).

Back

x^2 + 5x + 6.

Front

What is a binomial?

Back

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

Front

What is a trinomial?

Back

A trinomial is a polynomial that contains exactly three terms. For example, x^2 + 5x + 6 is a trinomial.

Front

How do you multiply a polynomial by a monomial?

Back

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