Solve the Problem $\mathrm { V }$ Be In $\mathrm { P } _ { 4 }$

Solve the problem.
-Let $\mathrm { V }$ be in $\mathrm { P } _ { 4 }$ , involving evaluation of polynomials at $- 4 , - 1,0,1$ , and 4 , and view $\mathrm { P } _ { 2 }$ by applying the Gram-Schmidt process to the polynomials 1 , $t$ , and $t ^ { 2 }$ .

A) $p _ { 2 } ( t ) = t ^ { 2 } - \frac { 34 } { 5 }$
B) $p _ { 2 } ( t ) = t ^ { 2 } + 6$
C) $\mathrm { p } _ { 2 } ( \mathrm { t } ) = \mathrm { t } ^ { 2 } + \frac { 34 } { 5 }$
D) $\mathrm { p } _ { 2 } ( \mathrm { t } ) = \mathrm { t } ^ { 2 } - \frac { 17 } { 6 }$