Question

Complete the square. Fill in the number that makes the polynomial given below, a perfect-square quadratic.x²-12x+

Answer 1

We are given the first two terms x^2 - 12x and we need the third term to make it a perfect square trinomial.

A perfect square trinomial results from squaring a binomial. It is in the form:

`(x+y)^2=x^2+2xy+y^2`

So to find the third term, we divide the second term by twice the square root of the first term.

Square root of the first term = x

Twice the square root of the first term = 2x

Second term = -12x

`(-12x)/(2x)=-6`

Then, we square the answer.

`(-6)^2=36`

The third term, then, must be 36.