Question
Factor the expression completely. \[ -4 x^{3}+6 \]
Ask by Ray Ryan. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression \(-4x^{3}+6\) factors to \(-2(2x^{3}-3)\).
Solution
Factor the expression completely \( -4x^3+6 \).
Factor the expression by following steps:
- step0: Factor:
\(-4x^{3}+6\)
- step1: Factor the expression:
\(-2\left(2x^{3}-3\right)\)
The expression \(-4x^{3}+6\) can be factored completely as \(-2(2x^{3}-3)\).
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Simplify this solution The Deep Dive
To factor the expression \( -4x^{3} + 6 \), we can first take out the greatest common factor, which is -2. This gives us: \[ -2(2x^{3} - 3) \] Next, we can see if the quadratic \( 2x^{3} - 3 \) can be factored further. Since it is a cubic expression, it doesn't factor neatly with integers, and it doesn't present a clear opportunity for factoring further (like a difference of squares or a perfect square). Thus, the completely factored form of the expression is: \[ -2(2x^{3} - 3) \]
