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.