Given that

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

find each of the following.

a)

g (-6)

b)

g (p+2)

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

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