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Find the quadratic polynomial that completes the factorization. $\newline$ $t^3 + 1 = (t + 1)(\_\_\_\_\_)$

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Factor sums and differences of cubes

Full solution

Q. Find the quadratic polynomial that completes the factorization.

\newline

t^3 + 1 = (t + 1)(\_\_\_\_\_)

Recognize as sum of cubes: To factor $t^3 + 1$ , we recognize it as a sum of cubes, which factors as $(t + 1)(t^2 - t + 1)$ .
Expand and check equality: Now we check if $(t + 1)(t^2 - t + 1)$ equals $t^3 + 1$ by expanding the factors. $\newline$ $(t + 1)(t^2 - t + 1) = t^3 - t^2 + t + t^2 - t + 1 = t^3 + 1$ .

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