Question

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

Explanation:

Step1: Recall factoring formula

For a quadratic polynomial \(ax^{2}+bx + c\) (\(a = 1\) here, \(b=-16\), \(c = 48\)), we need to find two numbers \(m\) and \(n\) such that \(m + n=b\) and \(mn=c\).

Step2: Find two - numbers

We need 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 factored form

The factored form of the quadratic polynomial \(x^{2}-16x + 48\) is \((x - 4)(x - 12)\).

Answer:

\((x - 4)(x - 12)\)