Explain what the following statement means: polynomials are closed under the operations of addition and subtraction. provide one addition example and one subtraction example to demonstrate.

After the addition and subtraction of any polynomial with the other polynomial the outcome is a polynomial. The below example is the prove of above statement.

The statement "Polynomial are closed under the operations of addition and subtraction" means that when the addition or subtraction of any polynomial with other polynomial is carried out the outcome is a polynomial.

Example: Add and subtract the polynomial given below-

  and  

Addition:

Subtraction:

So, from the above example it can be concluded that after the subtraction and addition of the polynomial the outcome is a polynomial.

For more information, refer the link given below:

link

i'm not sure i quite understand, could you provide more information?

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.