In each part express the vector as a linear combination of $p_1=2+x+4x^2,p_2=1-x+3x^2,$ and $p_3=3+2x+5x^2.$

$($a$)-9-7x-15x^2$

$($b$)6+11x+6x^2$

$($c$)0$

$($d$)7+8x+9x^2$