1. **Stating the problem:** Factoring is the process of breaking down an expression into simpler expressions (factors) that, when multiplied together, give the original expression. 2. **Formula and rules:** Common factoring techniques include: - Factoring out the greatest common factor (GCF): $$a x + a y = a(x + y)$$ - Factoring trinomials: $$ax^2 + bx + c = (mx + n)(px + q)$$ where $m p = a$ and $n q = c$ and $m q + n p = b$ - Difference of squares: $$a^2 - b^2 = (a - b)(a + b)$$ - Perfect square trinomials: $$a^2 \, \pm \, 2ab \, + \, b^2 = (a \, \pm \, b)^2$$ 3. **Example:** Factor $$6x^2 + 9x$$ - Step 1: Find the GCF of 6 and 9, which is 3. - Step 2: Factor out 3: $$6x^2 + 9x = 3(2x^2 + 3x)$$ - Step 3: Check if the expression inside the parentheses can be factored further. Here, it cannot. 4. **Another example:** Factor $$x^2 + 5x + 6$$ - Step 1: Find two numbers that multiply to 6 and add to 5: 2 and 3. - Step 2: Write as $$(x + 2)(x + 3)$$ 5. **Summary:** To factor an expression, look for common factors first, then apply special formulas or trial and error for trinomials. Factoring helps simplify expressions and solve equations efficiently.