Factor by grouping.

x cubedx3minus−x squaredx2plus+44xminus−4

We need to factor the polynomial \( x^3 - x^2 + 4x - 4 \) by grouping.

### Step 1: Group the terms
Group the terms in pairs to factor them more easily:

\[
(x^3 - x^2) + (4x - 4)
\]

### Step 2: Factor out the greatest common factor (GCF) from each group
Factor out the GCF from each group:

\[
x^2(x - 1) + 4(x - 1)
\]

### Step 3: Factor out the common binomial
Now, we can see that both terms have a common factor of \( (x - 1) \). Factor this out:

\[
(x - 1)(x^2 + 4)
\]

### Conclusion
The polynomial \( x^3 - x^2 + 4x - 4 \) factors as \( (x - 1)(x^2 + 4) \).

Would you like any further explanation, or do you have any other questions?

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**Related Questions:**
1. How would you solve \( x^3 - x^2 + 4x - 4 = 0 \) using the factors?
2. What are the roots of the equation \( x - 1 = 0 \)?
3. Can \( x^2 + 4 \) be factored further over the real numbers?
4. What does factoring by grouping mean, and when is it used?
5. How do you check if your factorization is correct?

**Tip:** When factoring by grouping, always look for common factors in pairs of terms. This method is particularly useful when dealing with four-term polynomials.

Learn how to factor the polynomial x^3 - x^2 + 4x - 4 step-by-step using the grouping method. This problem demonstrates key concepts in polynomial factoring, including grouping terms and factoring out common factors. Suitable for high school students studying algebra.

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