Bài 1:Thu gọn và sắp xếp các hạng tử của đa thức theo lũy thừa giảm dần của biến:
a) A(x)=3x4-x2+5-x+2x2+1/3x3+x4-2
b)B(x)=-2x2+5x5-x4+4-3x2+2x4+x3-5x5
c)C(x)=2x3-x5+2x4-x2+3x5-2x2-x4+1
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a) \(P\left(x\right)=3x^3-x^2-2x^4+3+2x^3+x+3x^4-x^2-2x^4+3+2x^3+x+3x^4\)
\(=2x^4+7x^3-2x^2+2x+6\)
\(Q\left(x\right)=-x^4+x^2-4x^3-2+2x^2-x-x^3-x^4+x^2-4x^3-2+2x^2-x-x^3\)
\(=-2x^4-10x^3+6x^2-2x-4\)
b) \(P\left(x\right)+Q\left(x\right)=2x^4+7x^3-2x^2+2x+6-2x^4-10x^3+6x^2-2x-4\)
\(=-3x^3+4x^2+2\)
`@` `\text {Ans}`
`\downarrow`
`a)`
\(P(x) = 5x^3 + 3 - 3x^2 + x^4 - 2x - 2 + 2x^2 + x\)
`= x^4 + 5x^3 + (-3x^2 + 2x^2) + (-2x+x) + (3-2)`
`= x^4 + 5x^3 - x^2 - x + 1`
\(Q(x) = 2x^4 + x^2 + 2x + 2 - 3x^2 - 5x + 2x^3 - x^4\)
`= (2x^4 - x^4) + 2x^3 + (x^2 - 3x^2) + (2x-5x) + 2`
`= x^4 + 2x^3 - 2x^2 - 3x +2`
`b)`
`P(x)+Q(x) = (x^4 + 5x^3 - x^2 - x + 1) + (x^4 + 2x^3 - 2x^2 - 3x +2)`
`= x^4 + 5x^3 - x^2 - x + 1 + x^4 + 2x^3 - 2x^2 - 3x +2`
`= (x^4+x^4)+(5x^3 + 2x^3) + (-x^2 - 2x^2) + (-x-3x) + (1+2)`
`= 2x^4 + 7x^3 - 3x^2 - 4x + 3`
`P(x)-Q(x)=(x^4 + 5x^3 - x^2 - x + 1) - (x^4 + 2x^3 - 2x^2 - 3x +2)`
`= x^4 + 5x^3 - x^2 - x + 1 - x^4 - 2x^3 + 2x^2 + 3x -2`
`= (x^4 - x^4) + (5x^3 - 2x^3) + (-x^2+2x^2)+(-x+3x)+(1-2)`
`= 3x^3 + x^2 + 2x - 1`
`Q(x)-P(x) = (x^4 + 2x^3 - 2x^2 - 3x +2)-(x^4 + 5x^3 - x^2 - x + 1)`
`= x^4 + 2x^3 - 2x^2 - 3x +2-x^4 - 5x^3 + x^2 + x - 1`
`= (x^4-x^4)+(2x^3 - 5x^3)+(-2x^2+x^2)+(-3x+x)+(2-1)`
`= -3x^3 - x^2 - 2x + 1`
`@` `\text {Kaizuu lv u.}`
P(x) = 3x2 – 5 + x4 – 3x3 – x6 – 2x2 – x3
= – x6 + x4 + (– 3x3 – x3) + (3x2 – 2x2) – 5
= – x6 + x4 – 4x3 + x2 – 5.
= – 5+ x2 – 4x3 + x4 – x6
Và Q(x) = x3 + 2x5 – x4 + x2 – 2x3 + x –1
= 2x5 – x4 + (x3 – 2x3) + x2 + x –1
= 2x5 – x4 – x3 + x2 + x –1.
= –1+ x + x2 – x3 – x4 + 2x5
a) \(...=P\left(x\right)=2x^4-x^4+3x^3+4x^2-3x^2+3x-x+3\)
\(P\left(x\right)=x^4+3x^3+x^2+2x+3\)
\(...=Q\left(x\right)=x^4+x^3+3x^2-x^2+4x+4-2\)
\(Q\left(x\right)=x^4+x^3+2x^2+4x+2\)
b) \(P\left(x\right)+Q\left(x\right)=\left(x^4+3x^3+x^2+2x+3\right)+\left(x^4+x^3+2x^2+4x+2\right)\)
\(\Rightarrow P\left(x\right)+Q\left(x\right)=2x^4+4x^3+3x^2+6x+5\)
\(P\left(x\right)-Q\left(x\right)=\left(x^4+3x^3+x^2+2x+3\right)-\left(x^4+x^3+2x^2+4x+2\right)\)
\(\)\(\Rightarrow P\left(x\right)-Q\left(x\right)=x^4+3x^3+x^2+2x+3-x^4-x^3-2x^2-4x-2\)
\(\Rightarrow P\left(x\right)-Q\left(x\right)=2x^3-x^2-2x+1\)
a: A(x)=x^4+3x^3-2x^2+x+1
B(x)=2x^4-x^3+3x^2-4x-5
b: A(x)+B(x)
=x^4+3x^3-2x^2+x+1+2x^4-x^3+3x^2-4x-5
=3x^4+2x^3+x^2-3x-4
A(x)-B(x)
=x^4+3x^3-2x^2+x+1-2x^4+x^3-3x^2+4x+5
=-x^4+4x^3-5x^2+5x+6
a. Ta có: A(x) = x5 + x2 + 5x + 6 - x5 - 3x - 5
= x2 + 2x + 1 (0.5 điểm)
B(x) = x4 + 2x2 - 3x - 3 - x4 - x2 + 3x + 4 = x2 + 1 (0.5 điểm)
a.
\(P(x)=3x^3-x^2-2x^4+3+2x^3+x+3x^4\)
\(=(-2x^4+3x^4)+(3x^3+2x^3)-x^2+x+3\)
\(=x^4+5x^3-x^2+x+3\)
\(Q(x)=-x^4+x^2-4x^3-2+2x^2-x-x^3\)
\(=-x^4+(-4x^3-x^3)+(x^2+2x^2)-x-2\)
\(=-x^4-5x^3+3x^2-x-2\)
b.
\(P(x)+Q(x)=(x^4+5x^3-x^2+x+3)+(-x^4-5x^3+3x^2-x-2)\)
\(=(x^4-x^4)+(5x^3-5x^3)+(-x^2+3x^2)+(x-x)+(3-2)\)
\(=2x^2+1\)
c.\(H(x)=Q(x)+P(x)\)
\(\Rightarrow H(x)=2x^2+1=0\)
\(\Rightarrow2x^2+1=0\)
\(2x^2\) \(=-1\)
\(x^2\) \(=\frac{-1}{2}\)
mà \(x^2\ge0\)
\(\Rightarrow\)Đa thức \(H(x)=P(x)+Q(x)\)ko có nghiệm
học tốt
Nhớ kết bạn với mình đó
`@`\(P\left(x\right)=3x^5-5x^2+x^4-2x-x^5+3x^4-x^2+x+1\)
\(P\left(x\right)=\left(3x^5-x^5\right)+x^4+\left(-5x^2-x^2\right)+\left(-2x+x\right)+1\)
\(P\left(x\right)=2x^5+x^4-6x^2-x+1\)
`@`\(Q\left(x\right)=-5-3x^5-2x+3x^2-x^5+2x-3x^3-3x^4\)
\(Q\left(x\right)=\left(-3x^5-x^5\right)-3x^4-3x^3+3x^2+\left(2x-2x\right)-5\)
\(Q\left(x\right)=-4x^5-3x^4-3x^3+3x^2-5\)
`@`\(P\left(x\right)+Q\left(x\right)=\left(2x^5+x^4-6x^2-x+1\right)+\left(-4x^5-3x^4-3x^3+3x^2-5\right)\)
\(=-2x^5-2x^4-3x^3-3x^2-x-4\)
Lời giải:
a. $A(x)=(3x^4+x^4)+\frac{1}{3}x^3+(-x^2+2x^2)+(-x)+(5-2)$
$=4x^4+\frac{1}{3}x^3+x^2-x+3$
b. $B(x)=(5x^5-5x^5)+(-x^4+2x^4)+x^3+(-2x^2-3x^2)+4$
$=x^4+x^3-5x^2+4$
c. $C(x)=(-x^5+3x^5)+(2x^4-x^4)+(2x^3)+(-x^2-2x^2)+1$
$=2x^5+x^4+2x^3-3x^2+1$