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.

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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 \(-4\).

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Step3: Combine the factors

Putting it all together, we have factored the original expression completely.

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

Answer:

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