Factoring Polynomials
Factor polynomials completely in Grade 10 algebra. Apply GCF factoring, difference of squares, perfect square trinomials, and sum/difference of cubes to break down polynomial expressions.
Key Concepts
New Concept To completely factor a polynomial of two or more terms means to express it as a product of prime polynomial factors.
Why it matters Factoring is how we deconstruct complex expressions to reveal their simpler, fundamental components. Mastering this allows you to solve sophisticated equations, turning seemingly impossible problems into manageable steps.
What’s next Next, you’ll learn specific patterns to factor different types of polynomials, starting with the greatest common factor.
Common Questions
What is the strategy for factoring a polynomial completely?
Always factor out the GCF first. Then identify the form: trinomial (try AC method), difference of squares (a²-b²), perfect square trinomial, or sum/difference of cubes. Factor until prime.
How do you factor a difference of two squares?
a² - b² = (a + b)(a - b). Identify the square root of each term and apply the pattern. For example, x² - 25 = (x + 5)(x - 5).
How do you know when a polynomial is completely factored?
A polynomial is completely factored when all factors are either prime polynomials (cannot be factored further) or monomials. Check by multiplying factors back to confirm the original expression.