Đáp án:
Câu a : 4x3−5x2+6x+94x3−5x2+6x+9
=4x3+3x2−8x2−6x+12x+9=4x3+3x2−8x2−6x+12x+9
=(4x3+3x2)−(8x2+6x)+(12x+9)=(4x3+3x2)−(8x2+6x)+(12x+9)
=x2(4x+3)−2x(4x+3)+3(4x+3)=x2(4x+3)−2x(4x+3)+3(4x+3)
=(4x+3)(x2−2x+3)=(4x+3)(x2−2x+3)
Câu b : 5x3−12x2+14x−45x3−12x2+14x−4
=5x3−10x2−2x2+10x+4x−4=5x3−10x2−2x2+10x+4x−4
=(5x3−2x2)−(10x2−4x)+(10x−4)=(5x3−2x2)−(10x2−4x)+(10x−4)
=x2(5x−2)−2x(5x−2)+2(5x−2)=x2(5x−2)−2x(5x−2)+2(5x−2)
=(5x−2)(x2−2x+2)=(5x−2)(x2−2x+2)
Câu c : x3−5x2+2x+8x3−5x2+2x+8
=x3+x2−6x2−6x+8x+8=x3+x2−6x2−6x+8x+8
=(x3+x2)−(6x2+6x)+(8x+8)=(x3+x2)−(6x2+6x)+(8x+8)
=x2(x+1)−6x(x+1)+8(x+1)=x2(x+1)−6x(x+1)+8(x+1)
=(x+1)(x2−6x+8)=(x+1)(x2−6x+8)
=(x+1)[x2−2x−4x+8]=(x+1)[x2−2x−4x+8]
=(x+1)[x(x−2)−4(x−2)]=(x+1)[x(x−2)−4(x−2)]
=(x+1)(x−2)(x−4)=(x+1)(x−2)(x−4)
Câu d : 4x3+5x2+10x−124x3+5x2+10x−12
=4x3+8x2−3x2+16x−6x−12=4x3+8x2−3x2+16x−6x−12
=(4x3−3x2)+(8x2−6x)+(16x−12)=(4x3−3x2)+(8x2−6x)+(16x−12)
=x2(4x−3)+2x(4x−3)+4(4x−3)=x2(4x−3)+2x(4x−3)+4(4x−3)
=(4x−3)(x2+2x+4)
