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```latex
8.
\begin{tabular}{|ll|l|l|l|l|l|l|}
\hline \multicolumn{3}{|c|}{[tex]$15x^3 + 3x^2 - 3x$[/tex]} & A & B & C & D & \\
\hline A & & & & \\
\hline [tex]$3 \cdot 5x^2 x + 3x x - 3 \cdot 1 \cdot x$[/tex] & [tex]$3x$[/tex] & [tex]$3x(5x^2 + x - 1)$[/tex] & & N/A \\
\hline
\end{tabular}
```

Sagot :

GinnyAnsweridn
Sure, let's solve the problem step-by-step by factoring the given expression [tex]\(15x^3 + 3x^2 - 3x\)[/tex].

### Step 1: Identify the Common Factor in Each Term

First, we look for the greatest common factor (GCF) among the terms of the expression.

1. In the term [tex]\(15x^3\)[/tex]:
- Coefficient: 15
- Variable part: [tex]\(x^3\)[/tex]

2. In the term [tex]\(3x^2\)[/tex]:
- Coefficient: 3
- Variable part: [tex]\(x^2\)[/tex]

3. In the term [tex]\(-3x\)[/tex]:
- Coefficient: -3
- Variable part: [tex]\(x\)[/tex]

The GCF of the coefficients (15, 3, -3) is 3. For the variable part, the lowest power of [tex]\(x\)[/tex] across the terms is [tex]\(x\)[/tex].

So, the GCF of the entire expression is [tex]\(3x\)[/tex].

### Step 2: Factor Out the Common Factor

We now divide each term by [tex]\(3x\)[/tex] and rewrite the expression:

1. [tex]\(15x^3 \div 3x = 5x^2\)[/tex]
2. [tex]\(3x^2 \div 3x = x\)[/tex]
3. [tex]\(-3x \div 3x = -1\)[/tex]

This gives us the expression:

[tex]\[15x^3 + 3x^2 - 3x = 3x(5x^2 + x - 1)\][/tex]

### Step 3: Verify the Factored Expression

To make sure we've factored correctly, we can distribute [tex]\(3x\)[/tex] back through the expression inside the parentheses:

[tex]\[3x(5x^2) + 3x(x) - 3x(1) = 15x^3 + 3x^2 - 3x\][/tex]

Since this matches the original expression, our factorization is correct.

Thus, the factored form of the expression [tex]\(15x^3 + 3x^2 - 3x\)[/tex] is:

[tex]\[3x(5x^2 + x - 1)\][/tex]

This is the final answer.
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