Question

question
factor completely.
16x³ - 112x² - 25x + 175

Explanation:

Step1: Group terms

Group the first two terms and the last two terms:
$$(16x^{3}-112x^{2})+(-25x + 175)$$

Step2: Factor out GCF from each group

Factor out \(16x^{2}\) from the first group and \(-25\) from the second group:
$$16x^{2}(x - 7)-25(x - 7)$$

Step3: Factor out common binomial factor

Now, factor out the common binomial factor \((x - 7)\):
$$(16x^{2}-25)(x - 7)$$

Step4: Factor the difference of squares

Notice that \(16x^{2}-25\) is a difference of squares (\(a^{2}-b^{2}=(a + b)(a - b)\)) where \(a = 4x\) and \(b = 5\):
$$(4x + 5)(4x - 5)(x - 7)$$

Answer:

\((4x + 5)(4x - 5)(x - 7)\)