# The remainder when #2x^3 + 9x^2 + 7x + 3# is divided by x - k is 9, how do you find k?

##### 1 Answer

The remainder of dividing

#### Explanation:

If you attempt to divide

So if the remainder is

#2k^3+9k^2+7k+3 = 9#

Subtract

#2k^3+9k^2+7k-6 = 0#

By the rational root theorem, any rational roots of this cubic will be of the form

That means that the possible rational roots are:

#+-1/2# ,#+-1# ,#+-3/2# ,#+-2# ,#+-3# ,#+-6#

Let's try the first one:

#f(1/2) = 1/4+9/4+7/2-6 = (1+9+14-24)/4 = 0#

so

Divide by

#2k^3+9k^2+7k-6 = (2k-1)(k^2+5k+6) = (2k-1)(k+2)(k+3)#

So the possible solutions are: