what is the factored form of the polynomial?\n$x^{2}-12x + 27$?\n$(x + 4)(x + 3)$\n$(x - 4)(x + 3)$\n$(x +…

Explanation:

Step1: Identify the form of quadratic

For a quadratic polynomial (ax^{2}+bx + c) (here (a = 1), (b=-12), (c = 27)), we need to find two numbers (m) and (n) such that (m + n=b) and (m\times n=c).

Step2: Find the two - numbers

We need two numbers that add up to (- 12) and multiply to (27). The numbers are (-9) and (-3) since ((-9)+(-3)=-12) and ((-9)\times(-3)=27).

Step3: Write in factored form

The factored form of the quadratic polynomial (x^{2}-12x + 27) is ((x - 9)(x - 3)) using the formula (x^{2}+bx + c=(x + m)(x + n)) where (m) and (n) are the two numbers found.

Answer:

D. ((x - 9)(x - 3))