Review: Polynomials & Factoring

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. For example, 3x^2 + 2x - 5 is a polynomial.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means to express it as a product of its factors, which are polynomials of lower degrees. For example, factoring x^2 - 9 gives (x - 3)(x + 3).

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 - x, the degree is 3.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a^2 - b^2 = (a - b)(a + b). For example, x^2 - 16 can be factored as (x - 4)(x + 4).

Front

How do you multiply two binomials?

Back

To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last. For example, (x - 2)(x + 3) = x^2 + 3x - 2x - 6 = x^2 + x - 6.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in the term 5x^2, 5 is the coefficient.

Front

What is a term in a polynomial?

Back

A term in a polynomial is a single mathematical expression that can be a constant, a variable, or a product of both. For example, in 3x^2 + 2x - 5, the terms are 3x^2, 2x, and -5.

Front

What is the sum of two polynomials?

Back

The sum of two polynomials is found by combining like terms. For example, (2x^2 + 3x) + (4x^2 - 5) = 6x^2 + 3x - 5.

Front

What is the product of a polynomial and a monomial?

Back

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

Front

What is a binomial?

Back

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