Question

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?​

Answer 1

The value of k is -8.

Step-by-step explanation:

To find the value of k, we need to use the remainder theorem. The remainder theorem states that if a polynomial f(x) is divided by x + a, then the remainder is equal to f(-a).

In this case, we are given that the remainder when f(x) = 3x^2 + 9x + k is divided by x + 1 is -14. So we have:

f(-1) = -14

Substituting x = -1 into the equation for f(x), we get:

3(-1)^2 + 9(-1) + k = -14

Simplifying this equation gives:

3 - 9 + k = -14

k = -8

Answer 2

The answer is 3. k = 3

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