Answer:
(x + 0.5) (x² - 0.5x + 0.25)
Step-by-step explanation:
x³ + 1/8
We can rewrite 1/8 as a decimal: 0.125
the cubed root of 0.125 then is 0.5; recalling that 5³ yields 125
Knowing this then, we can factor out our expression
(ax + b) (ax² − abx + b² ) = ax³ + b³, where a and b are coefficients.
If a = 1, and b we found to = 0.5, our expression becomes
(x + 0.5) (x² - 0.5x + 0.25)
We cannot further factor x² - 0.5x + 0.25, so our answer remains
(x + 0.5) (x² - 0.5x + 0.25)
Check via foiling
(x * x²) + (x * -0.5x) + (x * 0.25) + (0.5 * x²) + (0.5 * -0.5x) + (0.5 * 0.25)
x³ - 0.5x² + 0.25x + 0.5x² - 0.25x + 0.125 Combine like terms
x³ + 0.125 = x³ + 1/8
