Factor 2x³ − 16
Worked out line by line the way a teacher would write it.
Answer
| Factored form | 2(x − 2)(x² + 2x + 4) |
Step-by-step solution
4 steps-
1 Given2 x^{3} - 16
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2 Factor out the greatest common factor 2
2 divides every term, so it can be written once in front of a bracket. This is the distributive property used backwards: ab + ac = a(b + c).
2 \left(x^{3} - 8\right)Every term is divisible by 2.
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3 Sum/difference of cubes: a³ ± b³ = (a ± b)(a² ∓ ab + b²)
Sums and differences of cubes have their own pattern: a³ − b³ = (a − b)(a² + ab + b²) and a³ + b³ = (a + b)(a² − ab + b²).
\left(x - 2\right) \left(x^{2} + 2 x + 4\right) -
4 Fully factored form2 \left(x - 2\right) \left(x^{2} + 2 x + 4\right)
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