Simplify [tex]-2x^3 + 2x^2 - 3x + x^2 + 4 - x - 3x^2[/tex].

A. [tex]-2x^2 + x + 4[/tex]
B. [tex]-2x^3 + x^2 - 4x + 4[/tex]
C. [tex]-2x^3 - 4x + 4[/tex]
D. [tex]-2x^2 - 4x + 4[/tex]



Answer :

Let's simplify the expression \( -2x^3 + 2x^2 - 3x + x^2 + 4 - x - 3x^2 \) step by step by combining like terms.

### Step 1: Group and Identify Like Terms
Group the terms involving the same powers of \(x\):
1. Terms involving \(x^3\): \( -2x^3 \)
2. Terms involving \(x^2\): \( 2x^2 + x^2 - 3x^2 \)
3. Terms involving \(x\): \( -3x - x \)
4. Constant terms: \( 4 \)

### Step 2: Combine Like Terms

1. For \(x^3\):
[tex]\[ -2x^3 \][/tex]

2. For \(x^2\):
[tex]\[ 2x^2 + x^2 - 3x^2 = 2x^2 + 1x^2 - 3x^2 = 3x^2 - 3x^2 = 0 \][/tex]

3. For \(x\):
[tex]\[ -3x - x = -4x \][/tex]

4. Constant term remains the same:
[tex]\[ 4 \][/tex]

### Step 3: Write the Simplified Expression

Combine all the simplified terms:
[tex]\[ -2x^3 + 0x^2 - 4x + 4 \][/tex]
Since \(0x^2\) does not contribute anything, we can omit it:
[tex]\[ -2x^3 - 4x + 4 \][/tex]

So, the simplified expression is \(-2x^3 - 4x + 4\).

### Step 4: Match with the Given Options

Now, let's match the simplified expression with the given options:
1. \( -2x^2 + x + 4 \)
2. \( -2x^3 + x^2 - 4x + 4 \)
3. \( -2x^3 - 4x + 4 \)
4. \( -2x^2 - 4x + 4 \)

The simplified expression \(-2x^3 - 4x + 4\) matches option 3.

### Conclusion

The correct option is:
[tex]\[ \boxed{-2x^3 - 4x + 4} \][/tex]