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Question ID: 1179136

Match each trinomial on the left with its correctly factored form on the right. Some answer choices on the right will not be used.

[tex]\[
\begin{array}{l}
5x^3 - 20x^2 - 160x \\
5x^3 - 70x^2 - 160x \\
5x^3 + 20x^2 - 160x \\
5x^3 + 70x^2 - 160x
\end{array}
\][/tex]

[tex]\[
\begin{array}{l}
5x(x - 8)(x - 4) \\
5x(x + 8)(x - 4) \\
5x(x - 16)(x + 2) \\
5x(x + 16)(x - 2) \\
5x(x + 8)(x + 4) \\
5x(x - 8)(x + 4)
\end{array}
\][/tex]



Answer :

GinnyAnswer
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.

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