Factoring Polynomials Basics

Study Notes

Polynomial Basics

A polynomial consists of terms or a singular term with whole number exponents on variables.
Examples of polynomials include x^2 + 3x and 4y^3 - 2y + 1.

Key Definitions

Factor: An integer or polynomial that divides another evenly. In algebra, factoring involves expressing a polynomial as a product of its prime factors.
Factoring is crucial for simplifying polynomial expressions and solving equations.

Factoring by Grouping

Recognize patterns within polynomial expressions to group terms effectively.
Use the method of factoring by grouping to simplify polynomials into products of binomials.

Example Factorizations

Factorization of jm + jn + km + kn results in (j + k)(m + n).
The expression ab + 2a + 3b + 6 can be factored to (a + 3)(b + 2).
The polynomial x^2 + xy - 2x - 2y simplifies to (x + y)(x - 2).

More Complex Factorizations

The expression mn - 4m - 5n + 20 factors as (m - 5)(n - 4).
For ab + 4 + a + 4b, the factored form is (a + 4)(b + 1).
The polynomial y^2 + 10z - 10y - yz can be factored to (y - z)(y - 10).

Higher Degree Polynomials

The expression n^3 - n^2 + 3n - 3 simplifies to (n^2 + 3)(n - 1).
For mr + ns - nr - ms, the factorization results in (m - n)(r - s).
The polynomial z^3 - 2z^2 + 9z - 18 factors to (z^2 + 9)(z - 2).

Important Notes

Factors should be listed alphabetically when placing into grids or completing factorization tasks.
Familiarity with common factorization patterns speeds up the simplification of more complex expressions.

Description

This quiz covers the essential concepts of polynomials, including key definitions and the method of factoring. Learn how to factor polynomials using techniques like grouping and recognize patterns for simplifying expressions. Test your understanding of these fundamental algebraic skills.