1. **State the problem:** Factor the trinomial $23x + 21x^2 - 20$ completely. 2. **Rewrite the polynomial in standard form:** $$21x^2 + 23x - 20$$ 3. **Identify coefficients:** - $a = 21$ - $b = 23$ - $c = -20$ 4. **Use the factoring method for trinomials $ax^2 + bx + c$:** Find two numbers that multiply to $a \times c = 21 \times (-20) = -420$ and add to $b = 23$. 5. **Find factors of -420 that add to 23:** The pair is $35$ and $-12$ because $35 \times (-12) = -420$ and $35 + (-12) = 23$. 6. **Rewrite the middle term using these factors:** $$21x^2 + 35x - 12x - 20$$ 7. **Group terms:** $$(21x^2 + 35x) + (-12x - 20)$$ 8. **Factor each group:** $$7x(3x + 5) - 4(3x + 5)$$ 9. **Factor out the common binomial:** $$(7x - 4)(3x + 5)$$ 10. **Final answer:** $$23x + 21x^2 - 20 = (7x - 4)(3x + 5)$$ This shows the polynomial is not prime and can be factored as above.