Factoring Polynomials
Factoring is polynomial division made visible. 'What multiplied together gives this expression?' Recognizing that x² − 9 = (x + 3)(x − 3) — the difference of squares — is a pattern worth internalizing. Factoring trinomials requires systematic thinking about factor pairs. This skill is prerequisite to solving quadratics and simplifying rational expressions.
What students explore
Factoring is polynomial division made visible. 'What multiplied together gives this expression?' Recognizing that x² − 9 = (x + 3)(x − 3) — the difference of squares — is a pattern worth internalizing. Factoring trinomials requires systematic thinking about factor pairs. This skill is prerequisite to solving quadratics and simplifying rational expressions.
Key ideas
Factor out the greatest common factor from a polynomial. Factor trinomials of the form x² + bx + c. Recognize and factor difference of squares: a² − b². Verify factoring by expanding.
Putting it together
Apply these ideas through worked examples, guided practice, and real-world problems.