x2−12x+144 Factor the perfect square trinomial.

Question

Factor the perfect square trinomial.

Answer 1

x²-12x + 144 = x²-12x +36 -36 + 144 = (x-6)² +108

x = 6 ± √-108 = 6 ± (6√3) i

(x+6 + (6√3) i)(x+6 - (6√3) i)

I don't see why they call it a perfect square trinomial unless the original expression is wrong.

A perfect square trinomial would be:

x²-24x + 144

For a perfect square trinomial ax²+bx+c, b² must equal 4ac, which it is not for the original equation.

Answer 2

a perfect square trinomial would have the form.

(a + b)² = a² + 2ab + b²

^{(x+12)^2 = x^2+2(12x) + 12^2}

x^2 + 24x + 144

OR

(a - b)² = a² - 2ab + b²

(x - 12) ^2 = x^2 - 2(12x) + 12^2

x^2 - 24x + 144