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Find the quadratic polynomial that completes the factorization. $\newline$ $c^3 + 8 = (c + 2)(\_\_\_\_\_)$

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Factor sums and differences of cubes

Full solution

Q. Find the quadratic polynomial that completes the factorization.

\newline

c^3 + 8 = (c + 2)(\_\_\_\_\_)

Recognize as sum of cubes: To factor $c^3 + 8$ , recognize it as a sum of cubes: $c^3 + 2^3$ .
Factor using sum of cubes formula: The sum of cubes can be factored as $(a + b)(a^2 - ab + b^2)$ where $a = c$ and $b = 2$ .
Plug in values: Plug in $a = c$ and $b = 2$ into the sum of cubes formula: $(c + 2)(c^2 - 2c + 4)$ .
Check multiplication: Check the multiplication to ensure it gives the original expression: c + \(2)(c^ $2$ - $2$ c + $4$ ) = c^ $3$ + $2$ c^ $2$ - $2$ c^ $2$ - $4$ c + $4$ c + $8$ = c^ $3$ + $8$ \

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