1. **State the problem:** We want to factor the expression $$3^{2x} + 3^x - 6$$ into the form $$(3^x + a)(3^x + b)$$ and find the values of $a$ and $b$. 2. **Rewrite the expression:** Notice that $$3^{2x} = (3^x)^2$$. Let $$y = 3^x$$. Then the expression becomes: $$y^2 + y - 6$$ 3. **Factor the quadratic:** We want to factor $$y^2 + y - 6$$ into $$(y + a)(y + b)$$ where $a$ and $b$ satisfy: - $a + b = 1$ (the coefficient of $y$) - $ab = -6$ (the constant term) 4. **Find $a$ and $b$:** - Factors of $-6$ that add up to $1$ are $3$ and $-2$ because $3 + (-2) = 1$ and $3 imes (-2) = -6$. 5. **Write the factorization:** $$y^2 + y - 6 = (y + 3)(y - 2)$$ 6. **Substitute back $y = 3^x$:** $$(3^x + 3)(3^x - 2)$$ 7. **Answer:** Comparing with $$(3^x + a)(3^x + b)$$, we have $a = 3$ and $b = -2$. **Final answer:** $a = 3$, $b = -2$ which corresponds to option 2.