539 cm^3

volume of the smaller cube is: 3•3•3 which equals 27.

volume of the bigger cube is: 8•8•8 which equals 512.

add those together and you get 539 cm^3

This will be a 4th degree polynomial. Our root of x = 7 in factorization form is (x-7). Our root of x = -11 in factorization form is (x+11) and the last one is a complex number. According to the conjugate root theorem, if we have 2+8i, we also HAVE to have 2-8i. In factorization form that first one is (x-(2+8i)) which simplifies to (x-2-8i). Its conjugate in factorization form is (x-2+8i). Now we will FOIL all that out. Let's start with the (x-2-8i)(x-2+8i). That multiplies out to

. We have to combine like terms here to shorten that a bit.

. i^2 is equal to -1, and -1(64) = -64. Now we have

. That is

. Now let's FOIL in another factorization.

. That comes out to

. One more term to go!

. That, finally, is

.

**Answer:**

1 out of 4

**Step-by-step explanation:**

**Answer: Solved.**

**Step-by-step explanation: The calculations are as follows -**

**(12) **Given zeroes are 5, -3 and -1 + 3i. So, the other conjugate of -1 + 3i, i.e., -1 - 3i will also be a root of the polynomial. So the polynomial f(x) will be of degree 4 and is given by

**(13) **Given polynomial is

Now, we will substitute the rational numbers in place of 'x' and check whether the value of f(x) becomes zero or not.

We will see that

Also, the polynomial is not zero for any rational number.

**(14) **Given,

So,

Thus, the problems are solved.