Given f(x) = 3x^2 + 9x + k, and the remainder when f(x) is divided by X + 1 is -14, then what is the value of k?

Letf(x)=x3+x2+kx-15

By the remainder theorem, the remainder when f(x) is divided by (x-2)

will be

f(2)

So we have: 3=f(2)=8+4+2k-15=2k-3

Add 3 to both ends to get: 6 = 2k

Divide both sides by 2 and transpose to get:

k=3Left(x)=x3+x2+kx-15

By the remainder theorem, the remainder when

f ( x ) is divided by ( x − 2 ) will be f ( 2 )

So we have:

3 = f (2) = 8 + 4 + 2

k − 15 = 2

k − 3

Add 3

to both ends to get: 6 = 2 k

Divide both sides by 2

and transpose to get:

k = 3

answer:

c. the third graph