Question

What is the value of c so that x^2 + 17x + c is a perfect square trinomial?

Answer 1

We are dealing with a perfect square trinomial with a leading coefficient of 1.
That means that the coefficient of the x^2 term is 1.

\((x+a)^2 = (x + a)(x + a) = x^2 + ax + ax + a^2 = x^2 + 2ax + a^2\)

After we square the binomial ax + a, we get \(x^2 + 2ax + a^2\).
Notice that the middle term is 2ax.
The last term is a^2.
If you divide 2a by 2, you get a.
Then square a to get a^2.
That means if you take half of the middle coefficient and square it, you get the last term of a perfect square trinomial that has leading coefficient 1.

Answer 2

Thank you!

Answer 3

You're welcome.