Final answer:
To divide (5x⁴-2x³-7x²-39) by (x²+2x-4), the correct answer is 5x² - 12x + 22.
Step-by-step explanation:
To divide (5x⁴-2x³-7x²-39) by (x²+2x-4), we can use long division.
First, we divide the first term of the numerator (5x⁴) by the first term of the denominator (x²). This gives us 5x². We then multiply this quotient by the denominator (x²+2x-4) and subtract it from the numerator (5x⁴-2x³-7x²-39).
We repeat this process with the next term until we have no more terms left. The final quotient is the result of the division.
In this case, the correct answer is 5x² - 12x + 22 (option a).