Bài 1

) P ( x ) + Q ( x ) P(x)+Q(x) = ( x 4 − 5 x 3 + 4 x − 5 ) + ( − x 4 + 3 x 2 + 2 x + 1 ) =(x 4 −5x 3 +4x−5)+(−x 4 +3x 2 +2x+1) = x 4 − 5 x 3 + 4 x − 5 − x 4 + 3 x 2 + 2 x + 1 =x 4 −5x 3 +4x−5−x 4 +3x 2 +2x+1 = ( x 4 − x 4 ) − 5 x 3 + 3 x 2 + ( 4 x + 2 x ) + ( 1 − 5 ) =(x 4 −x 4 )−5x 3 +3x 2 +(4x+2x)+(1−5) = − 5 x 3 + 3 x 2 + 6 x − 4 =−5x 3 +3x 2 +6x−4 b) R ( x ) = P ( x ) − Q ( x ) R(x)=P(x)−Q(x) = ( x 4 − 5 x 3 + 4 x − 5 ) − ( − x 4 + 3 x 2 + 2 x + 1 ) =(x 4 −5x 3 +4x−5)−(−x 4 +3x 2 +2x+1) = x 4 − 5 x 3 + 4 x − 5 + x 4 − 3 x 2 − 2 x − 1 =x 4 −5x 3 +4x−5+x 4 −3x 2 −2x−1 = ( x 4 + x 4 ) − 5 x 3 − 3 x 2 + ( 4 x − 2 x ) + ( − 1 − 5 ) =(x 4 +x 4 )−5x 3 −3x 2 +(4x−2x)+(−1−5) = 2 x 4 − 5 x 3 − 3 x 2 + 2 x − 6 =2x 4 −5x 3 −3x 2 +2x−6

Bài 4

Thể tích của hình hộp chữ nhật đã cho là: V = x ( x − 1 ) ( x + 1 ) = x 3 − x V=x(x−1)(x+1)=x 3 −x b) Tại x = 4 x=4, thể tích của hình hộp chữ nhật là: V = 4 3 − 4 = 60 V=4 3 −4=60 (đơn vị thể tích)

Bài 3

2x 4 − 3 x 3 −3x 3 − 3 x 2 −3x 2 + 6 x +6x − 2 −2 x 2 − 2 x 2 −2 2 x 4 2x 4 − 4 x 2 −4x 2 2 x 2 − 3 x + 1 2x 2 −3x+1 − − − 3 x 3 −3x 3 + x 2 +x 2 + 6 x +6x − 2 −2 − 3 x 3 −3x 3 + 6 x +6x − − x 2 x 2 − 2 −2 x 2 x 2 − 2 −2 0 0 Vậy ta có phép chia hết và thương là Q = 2 x 2 − 3 x + 1 Q=2x 2 −3x+1.

Bài 2 5x(4x 2 −2x+1)−2x(10x 2 −5x+2)=−36 5 x . 4 x 2 + 5 x . ( − 2 x ) + 5 x . 1 + ( − 2 x ) . 10 x 2 + ( − 2 x ) . ( − 5 x ) + ( − 2 x ) . 2 = − 36 5x.4x 2 +5x.(−2x)+5x.1+(−2x).10x 2 +(−2x).(−5x)+(−2x).2=−36 20 x 3 + ( − 10 x 2 ) + 5 x + ( − 20 x 3 ) + 10 x 2 + ( − 4 x ) = − 36 20x 3 +(−10x 2 )+5x+(−20x 3 )+10x 2 +(−4x)=−36 ( 20 x 3 − 20 x 3 ) + ( − 10 x 2 + 10 x 2 ) + ( 5 x − 4 x ) = − 36 (20x 3 −20x 3 )+(−10x 2 +10x 2 )+(5x−4x)=−36 x = − 36 x=−36 Vậy x = −36