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morganalana17
factoring
Its the difference of cubes (since 216 is 6^3 and 1 is 1^3), so use the difference of cubes formula.
216x^3 - 1 = (6x)^3 - 1^3 Now, let 6x = a and let 1 = b a^3 - b^3 = (a - b)(a^2 + ab + b^2) So, just substitute for the a and the b. Can you do this part?
@morganalana17 ? Can you do this last part?
Once you get the function factored as indicated above, the second factor (which is a quadratic in x) cannot befactored any further for real solutions so you will have only one real soultion (one place where the x-axis is crossed). The function will of course have 2 more solutions but those will be imaginary solutions. The graph looks like:
(6x - 1)(36x^2 + 6x + 1)