What can we square to find 4*x*^{2} – 12*x* + *c*? We know whatever we're squaring, it will be riddled with question marks and look like (?*x* + ?). We'll need to work backwards, so turn around in your chair and bend your arms behind you. This will be tricky. We know that the coefficient on the *x* term must be 2 for us to find 4*x*^{2} after squaring. That's because we memorized our list of squares, thank you very much. The thing we're squaring looks like (2*x* + ?). To find -12*x* after squaring, the product 2*x*(?) must be -6*x*. Since we're squaring, the product of the outside terms will be the same as the product of the inside terms, so each product must be half of -12*x*. The missing number must be -3. That's because we memorized our basic multiplication table, thank you very much. (What do you mean, we sound kind of defensive?) Time to check: (2*x* – 3)^{2} = 4*x*^{2} – 12*x* + 9. The coefficients on the *x*^{2} and *x* terms work out, and now we know that *c* = 9. We had to square the term (2*x* – 3) to find it, but find it we did. |