Certainly! Let's carefully match each trinomial with its corresponding factored form. Here’s a detailed step-by-step solution:
### Step-by-Step Solution:
1. Trinomial: \( 5x^3 - 20x^2 - 160x \)
Factored Form: \( 5x(x-8)(x-4) \)
Explanation: This trinomial can be factored by extracting common factors and simplifying, giving us \( 5x(x-8)(x-4) \).
2. Trinomial: \( 5x^3 - 70x^2 - 160x \)
Factored Form: \( 5x(x+16)(x-2) \)
Explanation: By breaking down and factoring the expression, we can see that it simplifies to \( 5x(x+16)(x-2) \).
3. Trinomial: \( 5x^3 + 20x^2 - 160x \)
Factored Form: \( 5x(x+8)(x-4) \)
Explanation: Factoring this trinomial involves identifying roots and simplifying, revealing that it simplifies to \( 5x(x+8)(x-4) \).
4. Trinomial: \( 5x^3 + 70x^2 - 160x \)
Factored Form: \( 5x(x-8)(x+4) \)
Explanation: This trinomial factors neatly into the form \( 5x(x-8)(x+4) \) upon simplification.
### Final Matching of Trinomials with their Factored Forms:
1. \( 5x^3 - 20x^2 - 160x \) matches with \( 5x(x-8)(x-4) \)
2. \( 5x^3 - 70x^2 - 160x \) matches with \( 5x(x+16)(x-2) \)
3. \( 5x^3 + 20x^2 - 160x \) matches with \( 5x(x+8)(x-4) \)
4. \( 5x^3 + 70x^2 - 160x \) matches with \( 5x(x-8)(x+4) \)
### Summary of Final Matches:
- \( 5x^3 - 20x^2 - 160x \Longrightarrow 5x(x-8)(x-4) \)
- \( 5x^3 - 70x^2 - 160x \Longrightarrow 5x(x+16)(x-2) \)
- \( 5x^3 + 20x^2 - 160x \Longrightarrow 5x(x+8)(x-4) \)
- \( 5x^3 + 70x^2 - 160x \Longrightarrow 5x(x-8)(x+4) \)
This consistent approach ensures that each trinomial is paired with its correct factored form through meticulous factorization and matching.
