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.

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!