what is the factored form of the polynomial?\n$x^{2}-15x + 36$\n$(x - 4)(x - 9)$\n$(x - 3)(x - 12)$\n$(x +…

Explanation:

Step1: Recall factoring formula

For a quadratic polynomial (ax^{2}+bx + c) ((a = 1) here), we need to find two numbers (m) and (n) such that (m + n=b) and (m\times n = c). Here (b=- 15) and (c = 36).

Step2: Find two - numbers

We need to find two numbers that multiply to (36) and add up to (-15). The pairs of factors of (36) are: ((1,36)), ((2,18)), ((3,12)), ((4,9)), ((6,6)). Since we want a sum of (-15) and a product of (36), the numbers are (-3) and (-12) because ((-3)+(-12)=-15) and ((-3)\times(-12)=36).

Step3: Write factored form

The factored form of the quadratic polynomial (x^{2}-15x + 36) is ((x - 3)(x - 12)).

Answer:

B. ((x - 3)(x - 12))