To identify which expressions represent a quadratic expression in factored form, we need to look for expressions that are products of two binomials of the form [tex]\((x + a)(x + b)\)[/tex].
Let's examine each given expression one by one:
1. [tex]\( x^2 - x - 72 \)[/tex]:
- This is a quadratic polynomial, but it is not currently in factored form. Hence, it is not a factored quadratic expression.
2. [tex]\( (x+3)(x-7) \)[/tex]:
- This expression is in factored form and represents a quadratic expression. It can be expanded to [tex]\( x^2 - 4x - 21 \)[/tex].
3. [tex]\( 8(x+56) \)[/tex]:
- This expression is linear when expanded. The term [tex]\(8x + 448\)[/tex] is not a quadratic expression since there is no [tex]\(x^2\)[/tex] term. Therefore, it is not a quadratic expression in factored form.
4. [tex]\( (x+1)(x-2) \)[/tex]:
- This expression is in factored form and represents a quadratic expression. It can be expanded to [tex]\( x^2 - x - 2 \)[/tex].
5. [tex]\( (x-2) + (x+3) \)[/tex]:
- This expression simplifies to a linear expression [tex]\( 2x + 1 \)[/tex], which does not represent a quadratic expression.
Summarizing the analysis, the expressions that represent a quadratic expression in factored form are:
- [tex]\( (x+3)(x-7) \)[/tex]
- [tex]\( (x+1)(x-2) \)[/tex]
Therefore, the correct answers are:
- [tex]\( (x+3)(x-7) \)[/tex]
- [tex]\( (x+1)(x-2) \)[/tex]
