Question

Jeanie wrote the correct first step to divide 8z2 4z – 5 by 2z. what is the next step?

Answer 1

You write out the long division of polynomials the same as you do for dividing numbers. The dividend goes under the long division bar, while the divisor goes to the left.

1.  If you’re dividing $8z^2+4z-5$ by $2z,$ $8z^2+4z-5$ goes under the bar, while  $2z,$  goes to the left.

2. Divide the first term of the divisor into the first term of the dividend. The result of this division goes on top of the division bar.

For our example, dividing  $8z^2,$ the first term of the dividend, by $2z,$ the first term of the divisor, you would write $4z$ on the top of the division bar, over the $8z^2.$

3. Multiply the $4z$ in the quotient position by the divisor. Write the result of the multiplication under the leftmost terms of the dividend.

Continuing with our example, multiplying $2z$ by $4z$ produces  $8z^2.$ You would write this under the first two terms of the dividend.

And so on.

Answer 2

          4z + 2
2z      8z^2 + 4z - 5
       -  8z^2
                   4z - 5
               -   4z
                         -5

(8z^2 + 4z - 5) ÷ 2z = 4z + 2 R -5