6x^2 - 2 and 6x^2 + 2

which operation when performed on the two polynomials will not produce another polynomial.

addition

division

multiplication

subtraction

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If you add the two polynomials, you get

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

which is another polynomial.

We can rule out choice A.

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If you subtract the polynomials, the same kind of story happens (but you'll get a different polynomial)

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

The term -4 is a polynomial of degree 0.

We can rule out choice D.

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If you multiply the two polynomials, then you get another polynomial. Use the FOIL rule

(6x^2-2)(6x+2) = 36x^2 + 12x - 12x - 4 = 36x^2 - 4

or you could use the difference of squares rule to help expand

(6x^2-2)(6x+2) = (6x)^2 - (2)^2 = 36x^2 - 4

or you could use the box method (see Figure 1 in the attached images below)

Whichever method you use, the result is 36x^2 - 4 which is another polynomial.

We can rule out choice C. The only thing left is choice B.

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When dividing two polynomials, it is not always guaranteed to get another polynomial as a result. Use polynomial long division to calculate (6x^2-2)/(6x^2+2) and you'll get what you see in Figure 2 below. Figure 3 shows the long division table for (6x^2+2)/(6x^2-2). Both figures 2 and 3 show a nonzero remainder. The nonzero remainder means the result is not a polynomial.

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2

5   1/4   miles per hour

step-by-step explanation:

15   3/4 / 3 = 5   1/4