What is the quotient of (x^3+8)÷(x+2)

x² -2x +4

Step-by-step explanation:

You recognize the dividend as the sum of two cubes. The factorization of that is ...

... a³ + b³ = (a + b)(a² -ab +b²)

In your problem, you have a=x, b =2, so the factorization is ...

... (x³ +8) = (x +2)(x² -2x +4)

When this is divided by (x +2), the result is (x² -2x +4).

You can also use long division or synthetic division to get the same result.