Question
Factor the expression. (If the expression is not factorable using integers, enter PRIME.) \[ 2 x^{4}-2 \] SUBMIT ANSWER
Ask by Rose Robbins. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression factors to \( 2(x - 1)(x + 1)(x^2 + 1) \).
Solution
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Beyond the Answer
The expression \(2x^4 - 2\) can be factored by first taking out the common factor of 2: \[ 2(x^4 - 1) \] Now, \(x^4 - 1\) is a difference of squares, which can be further factored: \[ 2(x^2 - 1)(x^2 + 1) \] Next, \(x^2 - 1\) is another difference of squares: \[ x^2 - 1 = (x - 1)(x + 1) \] Putting it all together, the fully factored form is: \[ 2(x - 1)(x + 1)(x^2 + 1) \]
