1. **State the problem:** Simplify the expression $$5x + 8(2x - 3) - 14x + x^{2}$$ and then determine how many terms it has and identify the constant term. 2. **Apply the distributive property:** Multiply 8 by each term inside the parentheses: $$5x + 8 \times 2x - 8 \times 3 - 14x + x^{2} = 5x + 16x - 24 - 14x + x^{2}$$ 3. **Combine like terms:** Group the terms with $x$ and constants: $$ (5x + 16x - 14x) + x^{2} - 24 $$ 4. **Simplify the $x$ terms:** $$ (5 + 16 - 14)x + x^{2} - 24 = 7x + x^{2} - 24 $$ 5. **Rewrite the expression in standard form:** $$ x^{2} + 7x - 24 $$ 6. **Count the number of terms:** There are 3 terms: $x^{2}$, $7x$, and $-24$. 7. **Identify the constant term:** The constant term is $-24$. **Final answer:** The simplified expression is $$x^{2} + 7x - 24$$ with 3 terms and the constant term is $-24$.