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Question:

Select the correct answer from each drop-down menu. Rewrite the expression in factored form.

[tex]\[x^2 - 10x + 9 = (\square)(\square)\][/tex]

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Answer :

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]