Question

What is the remainder when (3x4 + 2x3 − x2 + 2x − 19) ÷ (x + 2)?

0
5
10
15

Answer 1

5

Step-by-step explanation:

Took the test :D--|--=:

Answer 2

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

`f(x)=3x^4+2x^3-x^2+2x-19`

And
`g(x)=x+2`

To find the remainder, we use the Remainder Theorem, which states that when f(x) is divided by (x-c) then the f(c) is the required remainder.

So,

Here, we have,

`x+2=0\\\\x=-2`

So, we will find f(-2) which will give us the required remainder,

`f(-2)=3(-2)^4+2(-2)^3-(-2)^2+2(-2)-19\\\\f(-2)=(3* 16)-(2* 8)- 4-4-19\\\\f(-2)=48-16-36-4-19\\\\f(-2)=5`

Hence, Second option is correct.