Which statement shows how two polynomials 5x − 6 and 6x + 2 demonstrate the closure property when multiplied?

30x2 − 26x − 12 may or may not be a polynomial

30x2 − 11x − 12 may or may not be a polynomial

30x2 − 26x − 12 is a polynomial

30x2 − 11x − 12 is a polynomial

Question

Which statement shows how two polynomials 5x − 6 and 6x + 2 demonstrate the closure property when multiplied? 

 30x2 − 26x − 12 may or may not be a polynomial 

 30x2 − 11x − 12 may or may not be a polynomial 

 30x2 − 26x − 12 is a polynomial 

 30x2 − 11x − 12 is a polynomial

freckles · Answer

First multiply

anonymous · Answer

wait can u give me an example im not quite sure how to multiply

anonymous · Answer

it

myininaya · Answer

so if i asked you to multiply 2x+1 and 4x-5
you would do the following:
by the way 2x+1 and 4x-5 and 5x-6 and 6x+2 are all polynomials by definition of a polynomial

so anyways multiplying 2x+1 and 4x-5

$$(2x+1)(4x-5)=2x(4x-5)+1(4x-5)\ =2x(4x)-2x(5)+1(4x)-1(5) \ =8x^2-10x+4x-5 \ =8x^2-6x-5$$

myininaya · Answer

is 8x^2-6x-5 a polynomial?

anonymous · Answer

no

myininaya · Answer

why would you say that

myininaya · Answer

do you know the definition of a polynomial?

myininaya · Answer

$$a_nx^n+a_{n-1}x^{n-1}+...+a_3x^3+a_2x^2+a_1x^1+a_0$$
where n is positive integer or zero
those ai (the coefficients can be zero)
the exponents all have to be positive integers or zero

myininaya · Answer

examples of polynomials:
1
5
x
x+1
x^2+2x+1
x^3-x-4
x^5+1
x^7
examples of an expression that is not polynomial:
x^-1
x^-1+2
sqrt(x)
|x|
x^2/3+1
1/x
-1/(x-1)


I could sit here and give you tons of examples of each
but you should get the idea of what is a polynomial now and what is not