Review: Polynomials - Factoring

Front

What is a polynomial?

Back

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

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 degree of a polynomial?

Back

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

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms.

Front

What is the difference of squares?

Back

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

Front

How do you factor a trinomial of the form x^2 + bx + c?

Back

To factor a trinomial of the form x^2 + bx + c, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n) where m and n are those numbers.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation ax² + bx + c = 0.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a polynomial that can be expressed as the square of a binomial, such as (a + b)² = a² + 2ab + b².

Front

What is the factor theorem?

Back

The factor theorem states that if f(c) = 0 for a polynomial f(x), then (x - c) is a factor of f(x).

Front

How do you factor by grouping?

Back

To factor by grouping, group terms with common factors, factor out the common factors, and then factor out the common binomial.