what is the factored form of the polynomial?\n$x^{2}-16x + 48$\n$(x - 4)(x - 12)$\n$(x - 6)(x - 8)$\n$(x +…

Explanation:

Step1: Analyze the quadratic form

For a quadratic polynomial (ax^{2}+bx + c) (here (a = 1), (b=-16), (c = 48)), 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 to find two numbers that add up to (-16) and multiply to (48). The numbers are (-4) and (-12) since (-4+( - 12)=-16) and (-4\times(-12) = 48).

Step3: Write the factored form

The factored form of the quadratic polynomial (x^{2}-16x + 48) is ((x - 4)(x - 12)) according to the formula (x^{2}+bx + c=(x + m)(x + n)) where (m) and (n) are the two numbers found.

Answer:

A. ((x - 4)(x - 12))