01 Key Concepts
Greatest Common Factor (GCF) Factoring
Find the largest factor shared by every term, then divide it out: 6x^2 + 9x = 3x(2x + 3).
Factoring Trinomials (a=1)
For x^2 + bx + c, find two numbers that multiply to c and add to b; those numbers become the factors: x^2+5x+6 = (x+2)(x+3).
Difference of Squares
a^2 - b^2 factors as (a+b)(a-b) — recognizable whenever you see two perfect squares separated by subtraction.
Perfect Square Trinomials
a^2 + 2ab + b^2 factors as (a+b)^2, and a^2 - 2ab + b^2 factors as (a-b)^2.
Checking Your Factoring
Multiply the factors back out (using FOIL or distribution) to confirm you get the original polynomial.
02 Key Formulas
- Difference of squares: a^2 - b^2 = (a+b)(a-b)
- Perfect square trinomial: a^2 + 2ab + b^2 = (a+b)^2
03 Solved Examples
Example 1 Factor 4x^2 + 12x using the GCF.
- Find the GCF of 4x^2 and 12x, which is 4x.
- Divide each term by 4x: 4x^2/4x = x, 12x/4x = 3.
- Write as 4x(x + 3).
Answer: 4x(x + 3)
Example 2 Factor x^2 + 7x + 12.
- Find two numbers that multiply to 12 and add to 7: 3 and 4.
- Write as (x+3)(x+4).
Answer: (x + 3)(x + 4)
Example 3 Factor x^2 - 16 using the difference of squares.
- Recognize x^2 and 16 as perfect squares (x^2 and 4^2).
- Apply the pattern a^2-b^2=(a+b)(a-b): (x+4)(x-4).
Answer: (x + 4)(x - 4)
04 Practice Questions
1Factor 3x^2 + 6x using the GCF.
3x(x+2)
2Factor x^2 + 5x + 6.
(x+2)(x+3)
3Factor x^2 - 9.
(x+3)(x-3)
4Factor x^2 - 8x + 15.
(x-3)(x-5)
5Factor x^2 + 10x + 25 (perfect square trinomial).
(x+5)^2
📄 Factoring — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.