Question

Please please please help i need help asap im so lost

if x^3 - 7x + 16x - 12 + (x-a) (x-b) (x-c) for all values of x, what is the value of abc?

Answer 1

$(x - a)(x - b)(x - c) \\ (x {}^{2} - bx - ax + ab)(x - c) \\ x {}^{3} - bx {}^{2} - ax {}^{2} + abx - cx {}^{2} + cbx + cax - abc$

$x {}^{3} + ( - a - b - c)x {}^{2} + (ab + cb + ca)x - abc$

$- a - b - c = - 7 \\ ab + ac + bc = 16 \\ - abc = - 12 \: \: \: \: \: abc = 12$

( a , b , c ) = ( 2 , 2 , 3 )