Given that
g(x)=3x2+2x+5

find each of the following.
a)
g(−6)
b)
g(p+2)

A) Substitute -6 for where x is in the expression...
g(-6) = 3(-6)^2 + 2(-6) + 5
g(-6) = 3(36) + 2(-6) + 5
g(-6) = 108 + 2(-6) + 5
g(-6) = 108 - 12 + 5
g(-6) = 96 + 5
g(-6) = 101

b) Substitute (p + 2) into where x is...
g(p + 2) = 3(p + 2)^2 + 2(p + 2) + 5
g(p + 2) = 3(p + 2)(p + 2) + 2(p + 2) + 5
g(p + 2) = 3(p^2 + 4p + 4) + 2(p + 2) + 5
g(p + 2) = 3p^2 + 12p + 12 + 2(p + 2) + 5
g(p + 2) = 3p^2 + 12p + 12 + 2p + 4 + 5
g(p + 2) = 3p^2 + 14p + 21

A.
sub -6 for x

g(-6)=3(-6)^2+2(-6)+5
g(-6)=3(36)-12+5
g(-6)=108-7
g(-6)=101

b.
sub p+2 for x
g(p+2)=3(p+2)^2+2(p+2)+5
g(p+2)=3(p^2+4p+4)+2p+4+5
g(p+2)=3p^2+12p+12+2p+9
g(p+2)=3p^2+14p+21