Add the proper constant to the binomial so that the resultin

Add the proper constant to the binomial so that the resulting trinomial is a perfect square. Then factor the trinom 2-16x +-- Add the proper constant to make a perfect square trinomial. x2-16x+ (Type an integer or a simplified fraction.)

Solution

x²-16x + ........

Using (a-b)²= a²-2ab+b²,

We can see that -16 = -2ab so ab = 8

Since a is 1 because the coefficient of x² is 1, we can find ‘b’ by using ab = 8

Now 1 x b = 8, Therefore b = 8

Now the equation would be : a²- 2ab + b²

= x² - 16x + 64