1.Cho hai đa thức :P(x)=`x^5-2x^3-x^5+x^4-5x+1+4x^2-3x^2+3x` Q(x)`=2x^3+x^4-2x^5-x^4+2x^5-x+5` 1)thu gọn và sắp xếp (giảm dần

2 bình luận về “1.Cho hai đa thức :P(x)=`x^5-2x^3-x^5+x^4-5x+1+4x^2-3x^2+3x` Q(x)`=2x^3+x^4-2x^5-x^4+2x^5-x+5` 1)thu gọn và sắp xếp (giảm dần”

1. Câu 1:

   1,   P(x) = x5 – 2×3 – x5 + x4 – 5x + 1 + 4×2 – 3×2 + 3x

               = (x5 – x5) + x4 – 2×3 + (4×2 – 3×2) + (5x + 3x)

               = x4 – 2×3 + x2 + 8x.

        Q(x) = 2×3 + x4 – 2×5 – x4 + 2×5 – x + 5

                = (-2×5 + 2×5) + x4 + 2×3 – x + 5

                = x4 + 2×3 – x + 5.

   2, P(x) + Q(x)= (x4 – 2×3 + x2 + 8x) + ( x4 + 2×3 – x + 5)

                        = x4 – 2×3 + x2 + 8x + x4 + 2×3 – x + 5

                        = (x4 + x4) + (-2×3 + 2×3) + x2 + (8x – x) + 5

                        = 2×4 + x2 + 7x + 5.

      P(x) – Q(x)= (x4 – 2×3 + x2 + 8x) – ( x4 + 2×3 – x + 5)

                      = x4 – 2×3 + x2 + 8x – x4 – 2×3 + x – 5

                      = (x4 – x4) + (-2×3 – 2×3) + x2 + (8x + x) – 5

                      = 4×3 + x2 + 9x – 5.

   Câu 2:

   Vì P(x) + Q(x)= 3×3 + 2×2 + 2

   ⇒            Q(x)= (3×3 + 2×2 + 2) – P(x)

                  Q(x)= (3×3 + 2×2 + 2) – (2×3 + x2 – 3x + 1)

                  Q(x)= 3×3 + 2×2 + 2 – 2×3 – x2 + 3x – 1

                  Q(x)= (3×3 – 2×3) + (2×2 – x2) + 3x + (2 – 1)

                  Q(x)= x3 + x2 + 3x + 1

        Vậy Q(x) = x3 + x2 + 3x + 1

   Vì P(x) – H(x)= x2 – 1

   ⇒          H(x)= P(x) – (x2 – 1)

                H(x)= (2×3 + x2 – 3x + 1) – (x2 – 1)

                H(x)= 2×3 + x2 – 3x + 1 – x2 + 1

                H(x)= 2×3 + (x2 – x2) – 3x + ( 1 + 1)

                H(x)= 2×3 – 3x + 2

         Vậy H(x) = 2×3 – 3x + 2.

   Trả lời
2. 1

   (1)P(x)=x^5-2x^3-x^5+x^4-5x+1+4x^2-3x^2+3x

   =(x^5-x^5)-2x^3+x^4-(5x-3x)+1+(4x^2-3x^2)

   =-2x^3+x^4-2x+1+x^2

   =x^4-2x^3+x^2-2x+1

   Q(x)=2x^3+x^4-2x^5-x^4+2x^5-x+5

   =2x^3+(x^4-x^4)-(2x^5-2x^5)-x+5

   =2x^3-x+5

   (2)

   P(x)+Q(x)=(x^4-2x^3+x^2-2x+1)+(2x^3-x+5)

   =x^4-2x^3+x^2-2x+1+2x^3-x+5

   =x^4-(2x^3-2x^3)+x^2-(2x+x)+(1+5)

   =x^4+x^2-3x+6

   P(x)-Q(x)=(x^4-2x^3+x^2-2x+1)-(2x^3-x+5)

   =x^4-2x^3+x^2-2x+1-2x^3-x+5

   =x^4-(2x^3+2x^3)+x^2-(2x-x)+(1-5)

   =x^4+4x^3+x^2-x-4

   Vậy P(x)+Q(x)=x^4+x^2-3x+6

   P(x)-Q(x)=x^4+4x^3+x^2-x-4

   2

   (1)P(x)+Q(x)=3x^3+2x^2+2

   =>Q(x)=(3x^3+2x^2+2)-(2x^3+x^2-3x+1)

   Q(x)=3x^3+2x^2+2-2x^3-x^2+3x-1

   Q(x)=(3x^3-2x^3)+(2x^2-x^2)+(2-1)+3x

   Q(x)=x^3+1+3x

   Vậy Q(x)=x^3+1+3x

   (2)P(x)-H(x)=x^2-1

   =>H(x)=P(x)-x^2-1

   H(x)=(2x^3+x^2-3x+1)-(x^2-1)

   H(x)=2x^3+x^2-3x+1-x^2+1

   H(x)=2x^3+(x^2-x^2)-3x+(1+1)

   H(x)=2x^3-3x+2

   Vậy H(x)=2x^3-3x+2

   Trả lời