Factor Quadratic 27E1Cc

1. **State the problem:** We want to factor the quadratic expression $$x^2 - x + \frac{2}{9}$$. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, we look for two numbers that multiply to $$ac$$ and add to $$b$$. 3. **Identify coefficients:** Here, $$a = 1$$, $$b = -1$$, and $$c = \frac{2}{9}$$. 4. **Calculate product $$ac$$:** $$1 \times \frac{2}{9} = \frac{2}{9}$$. 5. **Find two numbers that multiply to $$\frac{2}{9}$$ and add to $$-1$$:** - Possible pairs are limited because $$\frac{2}{9}$$ is positive and $$b$$ is negative, so both numbers must be negative. - Try $$-\frac{2}{3}$$ and $$-\frac{1}{3}$$: $$-\frac{2}{3} \times -\frac{1}{3} = \frac{2}{9}$$ and $$-\frac{2}{3} + -\frac{1}{3} = -1$$. 6. **Rewrite the middle term:** $$x^2 - x + \frac{2}{9} = x^2 - \frac{2}{3}x - \frac{1}{3}x + \frac{2}{9}$$. 7. **Group terms:** $$(x^2 - \frac{2}{3}x) + (-\frac{1}{3}x + \frac{2}{9})$$. 8. **Factor each group:** $$x(x - \frac{2}{3}) - \frac{1}{3}(x - \frac{2}{3})$$. 9. **Factor out common binomial:** $$(x - \frac{1}{3})(x - \frac{2}{3})$$. 10. **Final answer:** $$x^2 - x + \frac{2}{9} = \left(x - \frac{1}{3}\right)\left(x - \frac{2}{3}\right)$$. This is the factored form of the quadratic expression.