If n = 2 + 6m and p = 2/n, what is the value of p when m = -1/2?

p = - 2

Step-by-step explanation:

Given

n = 2 + 6m ← substitute m = - into the expression

n = 2 + 6(- ) = 2 - 3 = - 1

Thus

p = = = - 2

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81