Factoring Basics 48D01B

1. **Understanding the problem:** Factoring means rewriting an expression as a product of simpler expressions called factors. 2. **Common factoring methods:** - Factoring out the greatest common factor (GCF). - Factoring trinomials of the form $$ax^2 + bx + c$$. - Factoring difference of squares: $$a^2 - b^2 = (a - b)(a + b)$$. - Factoring 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 $$6x^2$$ and $$9x$$, which is $$3x$$. - Step 2: Factor out $$3x$$: $$6x^2 + 9x = 3x(\cancel{2x} + \cancel{3})$$ - Step 3: Simplify inside the parentheses: $$3x(2x + 3)$$ 4. **Example: Factor $$x^2 + 5x + 6$$** - Step 1: Find two numbers that multiply to $$6$$ and add to $$5$$: these are $$2$$ and $$3$$. - Step 2: Write as: $$x^2 + 2x + 3x + 6$$ - Step 3: Group terms: $$(x^2 + 2x) + (3x + 6)$$ - Step 4: Factor each group: $$x(x + 2) + 3(x + 2)$$ - Step 5: Factor out common binomial: $$(x + 3)(x + 2)$$ 5. **Summary:** Factoring breaks expressions into products by identifying common factors or patterns. Practice with different expressions to get comfortable!