Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 3x^2 + 2x + 1 is a polynomial.

Front

What are like terms in a polynomial?

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

How do you combine like terms?

Back

To combine like terms, add or subtract the coefficients of the terms that have the same variable and exponent. For example, 3x + 5x = 8x.

Front

What is the degree of a polynomial?

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 + 5, the degree is 3.

Front

What is the difference between a monomial, binomial, and trinomial?

Back

A monomial has one term (e.g., 3x), a binomial has two terms (e.g., 3x + 2), and a trinomial has three terms (e.g., 3x^2 + 2x + 1).

Front

How do you simplify a polynomial expression?

Back

To simplify a polynomial expression, combine like terms and perform any necessary arithmetic operations. For example, simplify 2x + 3x - 4 to get 5x - 4.

Front

What is the process of adding polynomials?

Back

To add polynomials, combine like terms from each polynomial. For example, (2x + 3) + (4x + 5) = 6x + 8.

Front

What is the process of subtracting polynomials?

Back

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

Front

How do you multiply two binomials?

Back

To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last. For example, (a + b)(c + d) = ac + ad + bc + bd.

Front

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

Back

The result is x^2 - 3x + 2x - 6, which simplifies to x^2 - x - 6.