Question

Factor the expression completely.
minus, 3, plus, 3, x, to the power 5
−3+3x
5

Answer 1

To factor the expression \(-3 + 3x^5\), you can follow these steps:

1. **Factor out common terms**: Both terms in the expression \(-3\) and \(3x^5\) have a common factor of \(3\).

2. **Factor out \(3\)**:
\[
-3 + 3x^5 = 3(-1 + x^5)
\]

Now we can observe that \(-1 + x^5\) can be rewritten as \(x^5 - 1\).

3. **Factor \(x^5 - 1\)**: The expression \(x^5 - 1\) can be factored using the difference of powers:
\[
x^5 - 1 = (x - 1)(x^4 + x^3 + x^2 + x + 1)
\]

4. **Putting it all together**:
\[
-3 + 3x^5 = 3(-1 + x^5) = 3(x^5 - 1) = 3(x - 1)(x^4 + x^3 + x^2 + x + 1)
\]

Thus, the completely factored form of the expression \(-3 + 3x^5\) is:
\[
3(x - 1)(x^4 + x^3 + x^2 + x + 1)
\]