Question

What is the missing constant term in the perfect square that starts with x^2-12x

Answer 1

Essentially, we are trying to find the missing constant term of
`(x - a)^2` (remember that we are subtracting
`a` due to the negative sign in front of the second term). Let's expand this to see what we can work with:

`(x - a)^2`

• Set up

`x^2 - ax - ax + a^2 = x^2 - 2ax + a^2`

• FOIL and simplify

Now, we know the second term is
`12x`, so let's set the second term in the polynomial we just found equal to
`12x`:

`2ax = 12x`

• Set up

`2a = 12`

• Divide both sides of the equation by
  `x`

`a = 6`

• Divide both sides of the equation by 2

We have found
`a = 6`. We know the missing constant term is
`a^2`, according to the polynomial we found earlier. Thus, the missing term is:

`a^2 \Rightarrow 6^2 = 36`

The missing constant term is 36.