Question

What is the quotient (x3 + 8) ÷ (x + 2)?

Answer 1

x² - 2x + 4

Explanation:

Given

`(x^3+8)/(x+2)`

Note the numerator is a sum of cubes, that is

x³ + 8 = x³ + 2³ and factors as

(x + 2)(x² - 2x + 4)

Hence

`((x+2)(x^2-2x+4))/(x+2)`

Cancel the factor (x + 2) on the numerator/ denominator, thus

quotient is x² - 2x + 4

Answer 2

`{x}^(2) - 2x + 4`

EXPLANATION

We want to find the quotient when

`{x}^(3) + 8`

is divided by

`x + 2`

We carry out synthetic division to obtain:

After the synthetic division, I circled the coefficient of the quotient.

1 -2 4

Hence the quotient is:

`{x}^(2) - 2x + 4`