Answer:
Hence, the quotient is:
\(x^2+2x+4\)
Step-by-step explanation:
We have to determine the quotient of the expression:
(x^3 + 8) ÷ (x + 2)
The dividend of the expression is:
x^3+8
and the divisor is:
x+2
we can write our expression as:
\(=\dfrac{x^3+8}{x+2}\\\\=\dfrac{x^3+2^3}{x+2}\)
We know that:
\(a^3+b^3=(a+b)(a^2+ab+b^2)\)
Hence, we have our expression as:
\(=\dfrac{(x+2)(x^2+4+2x)}{x+2}\\\\=x^2+2x+4\)
Hence, the quotient is:
\(x^2+2x+4\)
