Question

factor.
$2z^2 - 5z + 3$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times3 = 6\) and add up to \(-5\). The numbers are \(-2\) and \(-3\) since \((-2)\times(-3)=6\) and \(-2 + (-3)=-5\).

Step2: Rewrite the middle term

Rewrite \(-5z\) as \(-2z-3z\) in the quadratic expression: \(2z^{2}-2z - 3z + 3\).

Step3: Group and factor

Group the first two terms and the last two terms: \((2z^{2}-2z)+(-3z + 3)\). Factor out the common factors from each group: \(2z(z - 1)-3(z - 1)\). Now factor out the common binomial factor \((z - 1)\): \((2z - 3)(z - 1)\).

Answer:

\((2z - 3)(z - 1)\)