Question

6 factor the following expression. ( x^2 + 14x + 48 ) a ( (x - 6)(x - 8) ) b ( (x + 6)(x - 8) ) c ( (x + 8)(x + 6) ) d ( (x + 8)(x - 6) )

Explanation:

Step1: Recall factoring trinomials

To factor \(x^2 + bx + c\), we find two numbers that multiply to \(c\) and add to \(b\). Here, \(b = 14\), \(c = 48\).

Step2: Find two numbers

Find two numbers that multiply to \(48\) and add to \(14\). The numbers \(6\) and \(8\) work (\(6\times8 = 48\), \(6 + 8 = 14\)).

Step3: Write the factors

So, \(x^2 + 14x + 48=(x + 6)(x + 8)\) (or \((x + 8)(x + 6)\) as multiplication is commutative).

Answer:

C. \((x + 8)(x + 6)\)