Question

Divide Using Long Polynomial Division (9x⁴-15x³+21x²+x+2)/(3x²+2):

a) 3x² - 5x + 3 + (4x - 7)/(3x² + 2)
b) 3x² - 5x + 3 + (5x - 7)/(3x² + 2)
c) 3x² - 5x + 3 + (4x + 7)/(3x² + 2)
d) 3x² - 5x + 3 + (5x + 7)/(3x² + 2)

Answer 1

To divide the polynomial (9x⁴-15x³+21x²+x+2) by (3x²+2) using long division, follow the steps of long division and divide the highest degree term by the highest degree term, multiply the denominator by the quotient, subtract this result from the numerator, and repeat until there are no more terms in the numerator. The final result is 3x² - 5x + 3 + (4x - 7)/(3x² + 2). Option a is the correct answer.

Step-by-step explanation:

To divide the polynomial (9x⁴-15x³+21x²+x+2) by (3x²+2) using long division, follow these steps:

1. First, divide the highest degree term of the numerator by the highest degree term of the denominator. In this case, divide 9x⁴ by 3x², which gives 3x².
2. Multiply the entire denominator by the quotient obtained in the previous step, which is 3x². This gives you 9x⁴+6x².
3. Subtract the result from the numerator. (9x⁴-15x³+21x²+x+2) - (9x⁴+6x²) = -15x³+15x²+x+2.
4. Bring down the next term from the numerator, which is 0.
5. Repeat steps 1-4 until there are no more terms in the numerator.

The final result after performing long division is 3x² - 5x + 3 + (4x - 7)/(3x² + 2). Therefore, option a) 3x² - 5x + 3 + (4x - 7)/(3x² + 2) is the correct answer.