Question

What are the linear factors of the quadratic expression \[ x^{2} - 4x - 5 \]?

Options

• \( (x - 5)(x + 1) \)

• \( (x + 5)(x - 1) \)

• \( (x - 5)(x - 1) \)

• \( (x + 5)(x + 1) \)

Answer 1

Splitting the middle term: \[ x^{2} - 5x + 1x - 5 = x(x - 5) + 1(x - 5) = (x - 5)(x + 1) \]. Hence the quadratic expression converts into the two linear factors \( (x - 5) \) and \( (x + 1) \).