Question

What are the quotient and remainder of (x^5-x^3+-5) divided by (x-2)

Answer 1

Answer:

x⁴+2x³ +3x²+6x +12 r. $\dfrac{19}{x-2}$

Step-by-step explanation:

You can do this through synthetic division. It is a shorthand way of dividing polynomials.

First you need to make your divisor equal to zero so you can solve for what goes into the division box:

x - 2 = 0 →     x = 2

The next step is to arrange your polynomials in descending powers. All missing terms, you will put in a zero.

x⁵ - x³ + (-5)   →  x⁵ + 0x⁴- x³ + 0x² + 0x + (-5)

Now you can proceed to synthetic division. Make an upside down division box with the divisor outside and the coefficients of the dividend listed, along with their sign. Leave a space below the divident

+2 |   +1     0     -1     0     0     -5

    |                                              

Next you bring down the first coefficient:

+2 |   +1     0     -1     0     0     -5

    |                                              

        +1    

Then you multiply it by the divisor and write the product under the next coefficient:

+2 |   +1     0     -1     0     0     -5

    |           +2                                  

        +1    

Next add the column and put the sum below it:

+2 |   +1     0     -1     0     0     -5

    |          +2                                  

        +1    +2

Then multiply again and repeat until you reach the last coefficient:

+2 |   +1     0     -1     0     0     -5

    |          +2    +4   +6   +12   +24

        +1    +2    +3   +6   +12    +19

Now that you have your results, add  in the x and their powers. The powers will start with the highest power but 1 less than the dividend. Since the dividend's highest power is 5, then the quotient's highest power will be 4. Then write it in descending order :

+1x⁴    +2x³    +3x²   +6x   +12   +19

Now the last coefficient is your remainder. So your results will be:

x⁴+2x³ +3x²+6x +12 r. $\dfrac{19}{x-2}$

Answer 2

Answer:

D on edge 2020

Step-by-step explanation: