Factoring

Factoring rewrites a sum as a product — it's multiplying in reverse, and it's the key that unlocks zeros, simplifying, and solving. Work in this order:

• GCF first — always pull out the greatest common factor: $6x^2 - 15x = 3x(2x - 5)$.
• Difference of two squares — $a^2 - b^2 = (a - b)(a + b)$, so $9m^2 - 100 = (3m - 10)(3m + 10)$.
• Trinomials — $x^2 + bx + c = (x + p)(x + q)$ where $p + q = b$ and $pq = c$.
• Factor completely — keep going until nothing else factors (often GCF then one of the patterns).

These are real, released Regents questions; factor each carefully and check by multiplying back.