Question

factor.\\( z^2 - 5z + 4 \\)

Explanation:

Step1: Find two numbers

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

Step2: Rewrite the middle term

Rewrite the quadratic expression \(z^{2}-5z + 4\) by splitting the middle term using the two numbers we found: \(z^{2}-z-4z + 4\).

Step3: Group and factor

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

Answer:

\((z - 1)(z - 4)\)