Fill in the number that makes the polynomial a perfect-square quadratic. z2 + 18z +

Answer 1

To make the polynomial z^2 + 18z + c a perfect square quadratic, you need to find the value of c such that the polynomial can be written as (z + a)^2 .

A perfect square quadratic takes the form:

(z + a)^2 =(z+a)*(z+a)= z^2 + 2az + a^2

Comparing this with z^2 + 18z + c , you can see that 2a = 18 , so a = 9 .

Now you need to calculate a^2 :

a^2 = 9^2 = 81

So, the value of c that makes the polynomial a perfect-square quadratic is 81. Thus, the polynomial is:

z^2 + 18z + 81

Answer 2

(z+b)^2 = z^2+2bz+b^2

Now, we have z^2 + 18z + ------

Our goal is to have (z+b)^2 => 18z = 2*b*z => 18 = 2b, b=9.

Then we need to have b^2 = 9^2 = 81.

z^2 + 18z+81 = (z+9)^2