Final answer:
The expression 8x³ - 2x² + x factors initially by pulling out a common x, resulting in x(8x² - 2x + 1). The quadratic within the parentheses does not factor easily with integer coefficients, so the final factored form is x(8x² - 2x + 1).
Step-by-step explanation:
To factor the polynomial 8x³ - 2x² + x, first we look for any common factors in each term. We can see that each term contains at least one x, so we can factor out an x:
x(8x² - 2x + 1)
Now we must factor the quadratic expression inside the parentheses. However, upon closer examination, we see that 8x² - 2x + 1 does not factor neatly into binomials with integer coefficients. It is a quadratic with real but irrational roots, and thus does not easily factor further over the integers. Therefore, the factored form of the original expression is:
x(8x² - 2x + 1)