Question

Watch help video Jse the long division method to find the result when 6x⁴ - 9x³ - x² - 20x + 21 s divided by 2x² + 3x + 4. If there is a remainder, express the result in the form q(x)+(r(x))/(b(x))

Answer 1

To divide 6x⁴ - 9x³ - x² - 20x + 21 by 2x² + 3x + 4 using long division, the quotient is 3x² - 3x - 17, and the remainder is 45x + 79. The result in the form q(x) + (r(x))/(b(x)) is 3x² - 3x - 17 + (45x + 79)/(2x² + 3x + 4).

Step-by-step explanation:

To find the result when dividing 6x⁴ - 9x³ - x² - 20x + 21 by 2x² + 3x + 4 using long division, you start by dividing the first term of the dividend by the first term of the divisor. In this case, 6x⁴ ÷ 2x² = 3x². Then, multiply the divisor 2x² + 3x + 4 by the quotient 3x², and subtract the result from the original dividend. Repeat this process until all terms have been divided.
The final quotient is 3x² - 3x - 17, and the remainder is 45x + 79. So, the result in the form q(x) + (r(x))/(b(x)) is 3x² - 3x - 17 + (45x + 79)/(2x² + 3x + 4).