To simplify the expression $5x - 4x^2 - 1 + x - 8x^2 + 7$, we combine like terms:

1. Group terms with the same powers of $x$:

   • For $x^2$: $-4x^2 - 8x^2 = -12x^2$
   • For $x$: $5x + x = 6x$
   • For constants: $-1 + 7 = 6$

2. Write the simplified expression: $-12x^2 + 6x + 6$

Thus, the simplified expression is:

Answer: A. $-12x^2 + 6x + 6$

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Related Questions:

1. How do you identify and combine like terms in algebraic expressions?
2. What is the role of coefficients in simplifying polynomial expressions?
3. How do you arrange terms in standard form for a polynomial?
4. Can you simplify $3x^2 - 7x + 2x^2 + 5x - 8$?
5. Why is it important to simplify expressions before solving equations?

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Tip: Always arrange terms in descending order of powers for clarity in polynomial expressions.