Question

what is the result of dividing x3−6 by x 2? responses x2−2x 4 14x 2 x squared minus 2 x plus 4 plus fraction numerator 14 over denominator x plus 2 end fraction x2 2x 4 2x 2 x squared plus 2 x plus 4 plus fraction numerator 2 over denominator x plus 2 end fraction x2−2x 4−14x 2 x squared minus 2 x plus 4 minus fraction numerator 14 over denominator x plus 2 end fraction x2 2x 4−2x 2

Answer 1

The result of dividing x³ - 6 by x + 2 is quotient of x² - 2x + 4 and remainder -14.

Explanation:

We can use polynomial long division to divide x³ - 6 by x + 2. The steps are as follows:

x² - 2x + 4

x + 2 | x³ + 0x² + 0x - 6

x³ + 2x²

----------

-2x² + 0x

-2x² - 4x

----------

4x - 6

4x + 8

-----

-14

Therefore, the quotient is x² - 2x + 4 and the remainder is -14. We can write the final answer as:

x³ - 6 = (x² - 2x + 4)(x + 2) - 14

Answer 2

The result of dividing
`x^(3) - 6` by
`x^(2)` is
`x - 6/x^(2)`, which includes a polynomial term and a fraction resulting from the non-divisible remainder.

Step-by-step explanation:

To divide the polynomial expression
`x^(3) - 6` by
`x^(2)`, we can perform polynomial long division or synthetic division. However, since the expression is not divisible in a way that results in a polynomial without a remainder, we will end up with a mixed expression that includes a polynomial and a fraction. We apply the division rule: divide each term of the numerator by the term in the denominator. The term
`x^(3)` divided by
`x^(2)` gives us x, and there is no term in the numerator equivalent to
`x^(2)` to divide, so we then proceed to the constant term which cannot be divided evenly by
`x^(2)`. This leaves us a remainder which we write as a fraction over the divisor
`x^(2)`.

So the result is x + (-6/
`x^(2)`) or simply x - 6/
`x^(2)`.