Final answer:
To subtract the polynomials (12x² + 6x – 4) and (7x² + 11x + 8), change the signs of the second polynomial and combine like terms, resulting in the answer 5x² – 5x – 12, which is option a).
Step-by-step explanation:
The question asks us to perform the subtraction of two polynomials: (12x² + 6x – 4) – (7x² + 11x + 8). To do this, we first change the sign of each term in the second polynomial and then combine like terms with the first polynomial:
• Change the signs: (12x² + 6x – 4) – 7x² – 11x – 8
• Combine like terms:
o For x² terms: 12x² – 7x² = 5x²
o For x terms: 6x – 11x = -5x
o For constant terms: – 4 – 8 = – 12
Combine all the terms to get the final answer: 5x² – 5x – 12, which corresponds to option a) 5x² – 5x – 12. Therefore, option a is the correct option in the final answer.