Polynomials & Factoring Review

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

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

Back

A monomial has one term, a binomial has two terms, and a trinomial has three terms.

Front

What is the zero-product property?

Back

The zero-product property states that if the product of two or more factors is zero, at least one of the factors must be zero.

Front

How do you factor a quadratic polynomial in the form ax^2 + bx + c?

Back

To factor a quadratic polynomial, find two numbers that multiply to ac (the product of a and c) and add to b. Use these numbers to split the middle term.

Front

What is the factored form of x^2 - 5x + 6?

Back

(x - 2)(x - 3) because -2 and -3 multiply to 6 and add to -5.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern: a^2 - b^2 = (a - b)(a + b).

Front

What is the sum of cubes formula?

Back

The sum of cubes can be factored using the formula: a^3 + b^3 = (a + b)(a^2 - ab + b^2).

Front

What is the product of sums and differences?

Back

The product of sums and differences can be factored as: (a + b)(a - b) = a^2 - b^2.