What can we square to find 4x^{2} – 12x + c? We know that whatever we're squaring is gonna look like (px + q). 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 4x^{2} after squaring. That's because we memorized our list of squares, thank you very much. So p = 2, and the thing we're squaring looks like (2x + q). Since our middle term is -12x after squaring, we know that 2x(q) + 2x(q) must be -12x. 2x(q) + 2x(q) = -12x 4xq = -12x The missing number must be q = -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: (2x – 3)^{2} = 4x^{2} – 12x + 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 (2x – 3) to find it, but find it we did. |