What is the remainder if the equation is divided by (x-5)

Question

(X)=2x^3-8x^2-5x-25 what is the reminder of f the equation is divided by (x-5)

Answer 1

If you divide 2x^3 -8x^2 -5x -25 by x-5 you will get 2x^2+2x+5 with a remainder of zero.

Answer 2

Just use long division.........remainder is 0

Answer 3

You can use long division to figure this out or you can use synthetic division. Synthetic division works if it's just x plus or minus some number (like this case is "x - 5") and it is much easier.

In long division, you just divide like it was an "old school" long division problem:

You ask what expression, multiplied by x (the x in "x - 5") gives me 2x³ (the 2x³ in the "2x³ - 8x² - 5x - 25") and the answer is 2x². So you put 2x² above and multiply it by the x and the -5 and put the answers below. Like this:

Now you subtract (which means you flip the sign and add) like this:

Notice that we bring down the next number.

Continue this until the end being super careful - its very easy to make a mistake. The remainder, obviously is what you have left over.

This is complicated and hard to explain in a few words. I'd be happy to meet with you free of charge for an initial visit to explain this as well as synthetic division.

Answer 4

I like to use synthetic division (where you write the root and the coefficients), but your teacher may want a different method:

  Root       Coefficients              

    5           2       -8       -5       -25

                          10       10        25      (multiply 5 by the previous lower #: (5x2), (5x2), (5x5)

                 2        2         5         0

                 (Add columns: 2+0 = 2, -8+10 = 2, -5+10 =5, -25+25)

The 0 at the end means that there is no remainder!!!!

Check: Try x = 1: (2(1) – 8(1) – 5(1) – 25) / (1 – 5) = -36/-4 = 9 Note: no remainder!!