Verified answer

use polynomial long division

so x-5 ) x^2 -7x+12

x(x - 5) = x^2 -5x

x^2 -7x - (x^2 -5x) = -2x

-2(x - 5) = -2x + 10

-2x +12 - (-2x + 10) =2

so (x^2-7x+12) divided by (x-5) = (x -2) + 2/(x-5)

the remainder is 2 then the remainder is put over what you are are divide by.

such that (x-5)((x -2) + 2/(x-5)) = x^2-7x+12

to divide by x - 5 do as usual division method or you can do short cut like below.......

just write x- 5 two times (as dividend is quadratic) & adjust terms like this...

(x- 5) (x - 5)

x(x - 5) -2(x - 5) +2 to make it = dividend =x^2 - 7x +12

quotient = x - 2

remainder = 2 ( on applying remainder theorem --- by putting zero of polynomial i.e x = 5 in given polynomial)................................answer

= x^7 - 7x^6 +12Xx^6[ Where divider is x to the power minus 5]

If the the divider is x-5, then it becomes like this:

(x-4)(x-3)(x-5)^-1

x - 2

___________

x-5 | x^2-7x+12

x^2-5x

-----------

-2x+12

-2x+10

----------

2

The answer is x-2 + 2/(x-5)

English please