Question

question
factor completely:
$-2x^2 + 26x - 44$

Explanation:

Step1: Factor out the GCF

First, identify the greatest common factor (GCF) of the terms \(-2x^2\), \(26x\), and \(-44\). The GCF of \(-2\), \(26\), and \(-44\) is \(-2\). Factor out \(-2\) from each term:
$$-2x^2 + 26x - 44 = -2(x^2 - 13x + 22)$$

Step2: Factor the quadratic trinomial

Now, factor the quadratic trinomial \(x^2 - 13x + 22\). We need two numbers that multiply to \(22\) and add up to \(-13\). The numbers \(-11\) and \(-2\) satisfy this because \((-11) \times (-2) = 22\) and \((-11) + (-2) = -13\). So, we can factor \(x^2 - 13x + 22\) as \((x - 11)(x - 2)\).

Putting it all together, the completely factored form is:
$$-2(x - 11)(x - 2)$$

Answer:

\(-2(x - 11)(x - 2)\)