Question

Factor this expression completely, then place the factors in the proper location on the grid.

x^3 + 1/8

Answer 1

(x + 0.5) (x² - 0.5x + 0.25)

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