Question

Factor the trinomial. $$x^{2}-12 x+36$$

Short answer

The factored form of the trinomial \(x^{2} - 12x + 36\) is \((x - 6)^{2}\).

Step-by-step solution

Identify the coefficients and constant

The trinomial given is \(x^{2} - 12x + 36\), where -12 is the coefficient of x and 36 is the constant.

Find two numbers that add up to -12 and multiply to 36

The two numbers that satisfy this condition are -6 and -6 because -6 + -6 = -12 and -6 * -6 = 36.

Factor the trinomial

Using the numbers identified in the previous step, the trinomial can be factored as \((x - 6) (x - 6)\)

Simplify the expression

Since both factors are identical, the simplified expression is \((x - 6)^{2}\)