Which two expressions are prime polynomials? x2 - 5x + 3 oxx - xy² – x2 - 7x + 6 2xy - 4x2y3 + 5x8y2 X4y3 - 3x3 + 4x2y2 - x wa

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.

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.