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

ANSWER

EXPLANATION

We want to find the quotient when

is divided by

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:

x² - 2x + 4

Step-by-step explanation:

Given

Note the numerator is a sum of cubes, that is

x³ + 8 = x³ + 2³ and factors as

(x + 2)(x² - 2x + 4)

Hence

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

quotient is x² - 2x + 4

$12. that is my answer.