Question

6. (2x4− x³ + 3x² − 1) ÷ (x + 1)

The 4 is to the fourth pwr

Solve in long division I don't get how symbolab is giving me a different answer ​

Answer 1

To solve the division (2x^4 - x^3 + 3x^2 - 1) ÷ (x + 1) using long division, divide the highest degree term of the dividend by the leading term of the divisor, then multiply the divisor by the result and subtract it from the dividend. the final quotient is 2x^3 - 3x^2 + 6x - 7 and the remainder is 6x^2 - 1.

Step-by-step explanation:

To solve the division (2x^4 - x^3 + 3x^2 - 1) ÷ (x + 1), we can use long division.

First, divide the highest degree term of the dividend (2x^4) by the leading term of the divisor (x), which gives 2x^3. Multiply the divisor (x + 1) by 2x^3 to get 2x^4 + 2x^3.

Subtract this result from the dividend to get (-3x^3 + 3x^2 - 1).

Now repeat the process with the new dividend (-3x^3 + 3x^2 - 1). Divide (-3x^3) by (x) to get -3x^2, multiply the divisor (x + 1) by -3x^2 to get -3x^3 - 3x^2, and subtract this result from the new dividend to get (6x^2 - 1).

Continue this process until there are no more terms left in the dividend.

In this case, the final quotient is 2x^3 - 3x^2 + 6x - 7 and the remainder is 6x^2 - 1.

So the long division result is (2x^3 - 3x^2 + 6x - 7) + (6x^2 - 1)/(x + 1).