Question

Perform long division for the expression (4x⁴ - 3x³ - 5x² - 30) / (x² - 3x - 4).

A) 4x² - x + 8
B) 4x² + x - 8
C) 4x² - x - 8
D) 4x² + x + 8

Answer 1

To find the quotient of the long division (4x⁴ - 3x³ - 5x² - 30) / (x² - 3x - 4), we sequentially divide, multiply and subtract the terms. The steps of long division show that the correct answer is 4x² - x - 8, which is option C.

Step-by-step explanation:

To perform long division for the expression (4x⁴ - 3x³ - 5x² - 30) / (x² - 3x - 4), we divide the first term of the polynomial numerator by the first term of the polynomial denominator and use the result to multiply the entire denominator. We then subtract this from the original numerator, bring down the next term, and repeat the process until we have gone through all terms in the numerator. The final quotient will not have any remainders involving x terms as they will all cancel out.

• Divide 4x⁴ by x², which is 4x².
• Multiply the entire divisor (x² - 3x - 4) by 4x² and subtract from the original numerator.
• Bring down the next term and repeat the process until all terms are accounted for.

Using this process, we get the quotient as 4x² - x - 8, which corresponds to option C.