Factor the expression completely.

Question

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: \[ 3(x - 1)(x^4 + x^3 + x^2 + x + 1) \]