Final answer:
The polynomial 9x(x-8)-(x-8) is factored by grouping, resulting in the factored form (x-8)(9x-1), using the distributive property to factor out the common binomial (x-8).
Step-by-step explanation:
To factor the polynomial completely by grouping, we start by recognizing that the same binomial, (x-8), is present in both terms. The expression is 9x(x-8)-(x-8). By grouping, we factor out the common binomial, resulting in (x-8) being multiplied by another expression. The factored form thus becomes:
(x - 8)(9x - 1)
To summarize, we first looked for a common factor in both terms, which was (x-8). This was factored out, leaving the two terms that when multiplied by (x-8) give the original polynomial. This is an application of the distributive property, which is a fundamental algebraic principle for factoring polynomials.