Question

1b ( x^2 - 5x + 4 )
common factor

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(4\) (the constant term) and add up to \(-5\) (the coefficient of \(x\)). The numbers are \(-1\) and \(-4\) since \((-1)\times(-4) = 4\) and \((-1)+(-4)=-5\).

Step2: Rewrite the middle term

Rewrite the quadratic expression \(x^{2}-5x + 4\) as \(x^{2}-x-4x + 4\).

Step3: Group and factor

Group the first two terms and the last two terms: \((x^{2}-x)+(-4x + 4)\). Factor out the common factors from each group: \(x(x - 1)-4(x - 1)\). Now, factor out the common binomial factor \((x - 1)\): \((x - 1)(x - 4)\).

Answer:

\((x - 1)(x - 4)\)