Question

Add the proper constant to the binomial so that the resulting trinomial is a perfect square z^(2)+22z

Answer 1

To make the trinomial z^2 + 22z a perfect square, we need to determine the constant term that, when added, will complete the square.

To find that constant term, we take half the coefficient of the linear term (22z) and square it.

Half of 22z is 11z, and squaring it gives (11z)^2 = 121z^2.

So, to complete the square and make the trinomial a perfect square, we need to add 121z^2.

z^2 + 22z + 121z^2 = 122z^2 + 22z

Now, the resulting trinomial z^2 + 22z + 121z^2 is a perfect square.

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