F(x) = x3 + ax2 + bx + c The roots of f(x) = 0 are 2, 3, and k.
When f(x) is divided by x - 1, the remainder is -8.
a) Find the value of k.
b) Find the remainder when f(x) is divided by x + 1.​

a) k = 5.

b) remainder = -52.

Explanation:

When x = 2:

4a + 2b + c + 8 = 0  (1)

When x = 3

9a + 3b + c  + 27= 0(2)

By the remainder theorem:

f(1) = -8 so

a + b + c + 1 = -8

a + b + c + 9 = 0(3)

Solving the system of equations:

equation (2) - equation (1) gives:

5a + b = -19

Equation (2)  - (3) gives

8a + 2b = -18

Solving the last 2 gives:

a = -10 and b = 31.

So from the first equation:

c= -4a - 2b - 8

c = -4(-10) - 2(31) - 8 = -30

So the function is:

f(x) =  x^3 - 10x^2 + 31x - 30

Now as the last term is -30 , because 2 roots are 2 and 3, making  2 factors (x-2) and (x- 3) the third factor is (x - 5),  so the other root is 5

a) k = 5.

When the function is divided by x + 1 , (f-1) is the remainder.

b) f(-1) = (-1)^3  - 10(-1)^2 + 31(-1) - 30

=  -1 + 10 - 31 - 30

= -52.

explanation:

let the different atoms be x and y. each with four protons and same mass will be represented as follows.

mass number is number of protons + number of neutrons.

            and  

since, it is given that one has a negative charge while the other is neutral. therefore, there will be increase in number of protons and the atom will be represented as follows.

according to periodic table, mass number of beryllium is 9 and it has atomic number 4 so, the atoms will be and .  

the protons and neutrons will be located inside the nucleus whereas the electrons will be revolving around the nucleus.  

a corroding iron, if that's one of your choices