Factoring a Polynomial
Factor polynomials by identifying GCF first, then applying grouping, trinomial factoring, or special product patterns. Master Grade 9 factoring strategies.
Key Concepts
Property Factoring a polynomial is the inverse of the Distributive Property. It rewrites a sum or difference of monomials as a product of factors.
Examples $6x^3 + 8x^2 2x = 2x(3x^2 + 4x 1)$ $9x^4y^2 9x^5y = 9x^4y(y x^2)$.
Explanation Think of this as 'un distributing'! You find the GCF of all the terms, pull it out to the front, and write what’s left over inside parentheses. It's a great way to simplify complex expressions.
Common Questions
What is the first step when factoring a polynomial?
Always check for a greatest common factor (GCF) first. Factor out the GCF before applying grouping or special product patterns.
How do you verify factoring is correct?
Multiply your factors back together using distribution. If the product matches the original polynomial exactly, the factoring is correct.
When is factoring used in algebra?
Factoring solves quadratic equations, simplifies rational expressions, and finds zeros of polynomial functions in Grade 9 algebra.