Adding/Subtracting/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^3 + 3x^2 - x + 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 does it mean to subtract polynomials?

Back

Subtracting polynomials involves changing the signs of the terms in the polynomial being subtracted and then combining 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, 2x^3 + 3x^2 + x + 5.

Front

How do you multiply two polynomials?

Back

To multiply two 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 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 are like terms?

Back

Like terms are terms in a polynomial that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms.

Front

What is the result of (x + 2)(x + 3)?

Back

The result is x^2 + 5x + 6.

Front

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

Back

The result is a^2 - b^2 (difference of squares).

Front

How do you combine like terms in the expression 3x^2 + 5x - 2x^2 + 4?

Back

Combine like terms to get x^2 + 5x + 4.