Đáp án:
Ta có: 2x3+ax+b2x3+ax+b
=2x3+2x2−2x2−2x+(a+2)x+a+2+b−a−2=2x3+2x2-2x2-2x+(a+2)x+a+2+b-a-2
=2x2(x+1)−2x(x+1)+(a+2)(x+1)+b−a−2=2x2(x+1)-2x(x+1)+(a+2)(x+1)+b-a-2
=(x+1)(2x2−2x+a+2)+b−a−2=(x+1)(2x2-2x+a+2)+b-a-2
Do 2x3+ax+b2x3+ax+b chia x+1x+1 dư −6-6
⇒b−a−2=−6⇔b−a=−4(1)⇒b-a-2=-6⇔b-a=-4(1)
Lại có: 2x3+ax+b2x3+ax+b
=2x3−4x2+4x2−8x+(a+8)x−(2a+16)+b+2a+16=2x3-4x2+4x2-8x+(a+8)x-(2a+16)+b+2a+16
=2x2(x−2)+4x(x−2)+(a+8)(x−2)+b+2a+16=2x2(x-2)+4x(x-2)+(a+8)(x-2)+b+2a+16
=(x−2)(2x2+4x+a+8)+b+2a+16=(x-2)(2x2+4x+a+8)+b+2a+16
Do 2x3+ax+b2x3+ax+b chia x−2x-2 dư 2121
⇒b+2a+16=21⇔2a+b=5(2)⇒b+2a+16=21⇔2a+b=5(2)
Từ (1)(2)(1)(2) ta có hệ phương trình:
{−a+b=−42a+b=5⇔{3a=9−a+b=−4⇔{a=3−3+b=−4⇔{a=3b=−1{-a+b=-42a+b=5⇔{3a=9-a+b=-4⇔{a=3-3+b=-4⇔{a=3b=-1
Vậy (a;b)=(3;−1)
