Question

when a polynomial 2x^3+3x^2+ax+b is divided by (x-2) leaves remainder 2 and (x+2) leaves remainder -2 find a and b​

Answer 1

Answer:

$x-2=0\\x=2\\ f(x)=2x^{3} +3x^{2} +ax+b\\0=2*2^{3}+3*2^2+a*2+b\\0=16+12+2a+b\\0=28+2a+b\\\\-28-2a=b\\Taking factor=  x+2\\x+2=0\\x= -2\\ f(x)=2x^{3} +3x^{2} +ax+b\\0=2*-2^{3}+3*-2^2+a*-2+b\\0=-16+12-2a+b\\4+2a=b\\4+2a=-28-2a\\4a=-24\\a=-6\\\\b=-28-2a\\b=-28-2*-6\\b=-28+12\\b=-16$