Answer and step-by-step explanation:
We will use long division to solve this.
First we see how many times 2z will go into 8z². It will go in 4 times; this will go above 4z in the answer.
Next we multiply through; 4z(2z) = 8z². We write this below the 8z² in the dividend. We subtract; this gives us 0, so it cancels. Bring down the next term, 4z.
See how many times 2z goes into 4z. It goes 2 times; this goes beside the 4z in the answer. (Since it is positive, we separate them by an addition sign.)
Multiply back through; 2(2z) = 4z. Subtracting this gives us 0, so they cancel. This leaves -5 as the remainder; this means our answer is
4z+2 - 5/2z.