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

Multiple Choice

Solve the problem.
-Let $\mathrm { V }$ be in $\mathrm { P } _ { 4 }$ , involving evaluation of polynomials at $- 5 , - 3,0,3$ , and 5 , and view $\mathrm { P } _ { 2 }$ by applying the Gram-Schmidt process to the polynomials $1 , t$ , and $t ^ { 2 }$ .

A) $\mathrm { p } _ { 2 } ( \mathrm { t } ) = \mathrm { t } ^ { 2 } - \frac { 68 } { 5 }$
B) $\mathrm { p } _ { 2 } ( \mathrm { t } ) = \mathrm { t } ^ { 2 } - \frac { 18 } { 5 }$
C) $\mathrm { p } _ { 2 } ( \mathrm { t } ) = \mathrm { t } ^ { 2 } - 10$
D) $\mathrm { p } _ { 2 } ( \mathrm { t } ) = \mathrm { t } ^ { 2 } + \frac { 68 } { 5 }$