To rewrite the expression [tex]\( x^2 - 10x + 9 \)[/tex] in factored form, follow these steps:
1. Identify the quadratic expression: In this case, it is [tex]\( x^2 - 10x + 9 \)[/tex].
2. Look for two numbers that multiply to the constant term (9) and add up to the coefficient of the linear term (-10). These two numbers are -9 and -1 because:
- [tex]\((-9) \times (-1) = 9\)[/tex]
- [tex]\((-9) + (-1) = -10\)[/tex]
3. Rewrite the quadratic expression using these two numbers as factors:
[tex]\[
(x - 9)(x - 1)
\][/tex]
So, the factored form of [tex]\( x^2 - 10x + 9 \)[/tex] is:
[tex]\[
(\boxed{x} - 9)(\boxed{x} - 1)
\][/tex]
