To rewrite the expression [tex]\( x^2 - 10x + 9 \)[/tex] in factored form, follow these steps:
1. Understanding the Problem: We need to factor the quadratic expression [tex]\( x^2 - 10x + 9 \)[/tex].
2. Identify the Coefficients:
- The coefficient of [tex]\( x^2 \)[/tex] is [tex]\( 1 \)[/tex].
- The coefficient of [tex]\( x \)[/tex] is [tex]\( -10 \)[/tex].
- The constant term is [tex]\( 9 \)[/tex].
3. Finding the Roots of the Quadratic Equation:
- We need to find two numbers that multiply to give the constant term [tex]\( 9 \)[/tex] and add to give the coefficient of [tex]\( x \)[/tex] which is [tex]\( -10 \)[/tex].
- These two numbers are [tex]\( -1 \)[/tex] and [tex]\( -9 \)[/tex], because
- [tex]\((-1) \times (-9) = 9\)[/tex]
- [tex]\((-1) + (-9) = -10\)[/tex]
4. Writing the Factored Form:
- Using the roots [tex]\( -1 \)[/tex] and [tex]\( -9 \)[/tex], the expression can be factored as:
[tex]\[
(x - 1)(x - 9)
\][/tex]
Therefore, the expression [tex]\( x^2 - 10x + 9 \)[/tex] in factored form is:
[tex]\[
(x - 9)(x - 1)
\][/tex]
So the correct answer is:
[tex]\[
(x - 9)(x - 1)
\][/tex]
