Bài 3:
a)
A(x)=5$x^{4}$- 5+ 6$x^{3}$+ $x^{4}$- 5x- 12
=(5$x^{4}$+ $x^{4}$)+ 6$x^{3}$- 5x+ (-5-12)
=6$x^{4}$+ 6$x^{3}$- 5x- 17
B(x)=8$x^{4}$+ 2$x^{3}$- 2$x^{4}$+ 4$x^{3}$- 5x- 15- 2$x^{2}$
=(8$x^{4}$- 2$x^{4}$)+ (2$x^{3}$+ 4$x^{3}$)- 2$x^{2}$- 5x- 15
=6$x^{4}$+ 6$x^{3}$- 2$x^{2}$- 5x- 15
b)
H(x)= A(x)+ B(x)
H(x)=(6$x^{4}$+ 6$x^{3}$-5x-17)+ (6$x^{4}$+ 6$x^{3}$- 2$x^{2}$- 5x-15)
=6$x^{4}$+ 6$x^{3}$-5x-17+ 6$x^{4}$+ 6$x^{3}$- 2$x^{2}$- 5x-15
=(6$x^{4}$+ 6$x^{4}$)+ (6$x^{3}$+ 6$x^{3}$)- 2$x^{2}$+ (-5x- 5x)+ (-17- 15)
=12$x^{4}$+ 12$x^{3}$- 2$x^{2}$- 10x- 32
G(x)= A(x)- B(x)
G(x)=(6$x^{4}$+ 6$x^{3}$-5x-17)- (6$x^{4}$+ 6$x^{3}$- 2$x^{2}$- 5x-15)
=6$x^{4}$+ 6$x^{3}$-5x-17- 6$x^{4}$- 6$x^{3}$+ 2$x^{2}$+ 5x+ 15
=(6$x^{4}$- 6$x^{4}$)+ (6$x^{3}$- 6$x^{3}$)+ 2$x^{2}$+ (-5x+ 5x)+ (-17+ 15)
=2$x^{2}$- 2
c) G(x)=2$x^{2}$- 2
Cho: 2$x^{2}$- 2=0
2$x^{2}$ =0+2
2$x^{2}$ =2
$x^{2}$ =2 : 2
$x^{2}$ =1⇒x²=1²
⇒x=1
Vậy đa thức này có 1 nghiệm: x=1
cho mik xin 5* và ctlhn
@chúc bn hok tốt
