1. The problem is to factor the quadratic expression $10x^2 + 33x - 7$. 2. We use the factoring method for quadratics of the form $ax^2 + bx + c$. 3. Multiply $a$ and $c$: $10 \times (-7) = -70$. 4. Find two numbers that multiply to $-70$ and add to $33$. These numbers are $35$ and $-2$. 5. Rewrite the middle term using these numbers: $10x^2 + 35x - 2x - 7$. 6. Group terms: $(10x^2 + 35x) + (-2x - 7)$. 7. Factor each group: $5x(2x + 7) - 1(2x + 7)$. 8. Factor out the common binomial: $(5x - 1)(2x + 7)$. 9. The factored form of $10x^2 + 33x - 7$ is $(5x - 1)(2x + 7)$. This completes the factoring of the first quadratic.