Adding, Subtracting, and Multiplying Polynomials

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 does it mean to add polynomials?

Back

Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power.

Front

What is the process for subtracting polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms.

Front

How do you multiply two polynomials?

Back

To multiply polynomials, use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial.

Front

What is a like term?

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.

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 4x^3 + 2x^2 - x, the degree is 3.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 5x^4 + 3x^2 - 2, the leading coefficient is 5.

Front

What is the result of (a + b)(a - b)?

Back

The result is a^2 - b^2, which is known as the difference of squares.

Front

What is the formula for the square of a binomial?

Back

The square of a binomial (a + b)^2 is equal to a^2 + 2ab + b^2.

Front

How do you simplify (x^2y)^5?

Back

To simplify (x^2y)^5, apply the power of a product rule: (x^2)^5 * (y)^5 = x^{10}y^5.