Question

question
factor completely:
$x^2(2x - 5) - 5x(2x - 5) + 4(2x - 5)$

Explanation:

Step1: Factor out the common binomial factor

Notice that each term has a common factor of \((2x - 5)\). We can factor that out first.
\[

$$\begin{align*} &x^{2}(2x - 5)-5x(2x - 5)+4(2x - 5)\\ =&(2x - 5)(x^{2}-5x + 4) \end{align*}$$

\]

Step2: Factor the quadratic trinomial

Now we need to factor the quadratic \(x^{2}-5x + 4\). We look for two numbers that multiply to \(4\) and add up to \(-5\). Those numbers are \(-1\) and \(-4\).
\[

$$\begin{align*} x^{2}-5x + 4&=x^{2}-x-4x + 4\\ &=x(x - 1)-4(x - 1)\\ &=(x - 1)(x - 4) \end{align*}$$

\]

Step3: Combine the factors

Putting it all together, we have factored the original expression completely.
\[
(2x - 5)(x - 1)(x - 4)
\]

Answer:

\((2x - 5)(x - 1)(x - 4)\)