ANSWER
[tex]{x}^{2} - 2x + 4[/tex]
EXPLANATION
We want to find the quotient when
[tex] {x}^{3} + 8[/tex]
is divided by
[tex]x + 2[/tex]
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:
[tex] {x}^{2} - 2x + 4[/tex]
Answer:
x² - 2x + 4
Step-by-step explanation:
Given
[tex]\frac{x^3+8}{x+2}[/tex]
Note the numerator is a sum of cubes, that is
x³ + 8 = x³ + 2³ and factors as
(x + 2)(x² - 2x + 4)
Hence
[tex]\frac{(x+2)(x^2-2x+4)}{x+2}[/tex]
Cancel the factor (x + 2) on the numerator/ denominator, thus
quotient is x² - 2x + 4
