Factor Quadratic 5Fb1Bf

1. **State the problem:** Factor the quadratic expression $$9x^2 + 17x - 2$$ into the product of two binomials. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, we look for two binomials of the form $$(mx + n)(px + q)$$ such that $$m imes p = a$$, $$n imes q = c$$, and $$m imes q + n imes p = b$$. 3. **Identify coefficients:** Here, $$a = 9$$, $$b = 17$$, and $$c = -2$$. 4. **Find factor pairs:** - Factors of $$a=9$$ are $$(9,1)$$ or $$(3,3)$$. - Factors of $$c=-2$$ are $$(1,-2)$$ or $$(-1,2)$$. 5. **Test each option:** - Option 1: $$(9x - 1)(x + 2)$$ expands to $$9x^2 + 18x - x - 2 = 9x^2 + 17x - 2$$ which matches. - Option 2: $$(9x + 1)(x - 2)$$ expands to $$9x^2 - 18x + x - 2 = 9x^2 - 17x - 2$$ which does not match. - Option 3: $$(3x + 1)(3x - 2)$$ expands to $$9x^2 - 6x + 3x - 2 = 9x^2 - 3x - 2$$ which does not match. - Option 4: $$(3x - 1)(3x + 2)$$ expands to $$9x^2 + 6x - 3x - 2 = 9x^2 + 3x - 2$$ which does not match. 6. **Conclusion:** The correct factorization is $$(9x - 1)(x + 2)$$. **Final answer:** $$(9x - 1)(x + 2)$$