Question

factor completely ( x^2 - bx + 42 ) (options are partially visible, likely factoring a quadratic with multiple - choice options)

Explanation:

Step1: Recall factoring rule

To factor \(x^2 - bx + c\), find two numbers that multiply to \(c\) and add to \(-b\). Here, the quadratic is \(x^2 - 6x - 40\) (assuming the middle term is \(-6x\) from the options, as the original text might have a typo). We need two numbers that multiply to \(-40\) and add to \(-6\).

Step2: Find the numbers

The numbers \(-10\) and \(4\) work: \(-10\times4 = -40\) and \(-10 + 4 = -6\).

Step3: Write the factors

So, \(x^2 - 6x - 40=(x - 10)(x + 4)\).

Answer:

D. \((x - 10)(x + 4)\)