Which expression is a prime polynomial? A.
x3 − bx2
B.
x2 − 4x − 12
C.
x4 + 8xy3
D.
x2 − b3

A polynomial is prime if it can not be factored into polynomials of lower degree also with integer coefficients.

For example, the first option:

x^3 + b*x^2 can be rewritten as:

(x - 0)*(x^2 + b*x)

So it is not prime.

The second option:

x^2 -4x - 12

Because here we can factor this into:

(x + 2)*(x - 6) = x^2 - 6x + 2*x - 12 = x^2  - 4x - 12

Now, the third option is a two variable polynomial, here the degree is equal to the sum of the degrees of both variables.

x^4 + 8*x*y^3

(x - 0)*(x^3 + 8*y^3)

So each side has a lower degree than the original polynomial, then it is not prime.

4th option:

x^2 - b^3

This can be written as:

(x + b^(3/2))*(x - b^(3/2))

Now, here we have a problem.

If for example, b = 1, this would not be a prime.

because 1^(3/2) = 1.

But if b^(3/2) is not an integer, then we can not factorize the initial polynomial into lower degree polynomials with only integer coefficients, then we can not be 100% sure that this is not a prime polynomial, then this is the correct option.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

where did you get them? if you picked from the grass, is is probably poisonous.

step-by-step explanation: