Question

perform the division.
$(x^2 - 10x + 9) \div (x - 9)$
the answer is \boxed{ }
(simplify your answer.)

Explanation:

Step1: Factor the numerator

We factor the quadratic expression \(x^2 - 10x + 9\). We need two numbers that multiply to \(9\) and add up to \(-10\). Those numbers are \(-9\) and \(-1\). So, \(x^2 - 10x + 9=(x - 9)(x - 1)\).

Step2: Perform the division

Now we have \(\frac{(x - 9)(x - 1)}{x - 9}\). Since \(x
eq9\) (to avoid division by zero), we can cancel out the common factor \((x - 9)\) from the numerator and the denominator. This leaves us with \(x - 1\).

Answer:

\(x - 1\)