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1: \(M\left(x\right)=A\left(x\right)-2B\left(x\right)+C\left(x\right)\)
\(=2x^5-4x^3+x^2-2x+2-2x^5+4x^4-2x^2+10x-6+C\left(x\right)\)
\(=4x^4-4x^3-x^2+8x-4+x^4+4x^3+3x^2-8x+\dfrac{67}{16}\)
\(=5x^4+2x^2+\dfrac{3}{16}\)
2: \(M\left(-0.5\right)=5\cdot\left(-\dfrac{1}{2}\right)^4+2\cdot\left(-\dfrac{1}{2}\right)^2+\dfrac{3}{16}=1\)
a) Sắp xếp các hạng tử của mỗi đa thức theo lũy thừa tăng của biến.
\(P\left(x\right)=3x^2-5+x^4-3x^3-x^6-2x^2-x^3\)
\(=x^2-5+x^4-4x^3-x^6\)
Sắp xếp : \(-5+x^2+x^4-4x^3-x^6\)
\(Q\left(x\right)=x^3+2x^5-x^4+x^2-2x^3+x-1\)
\(=-x^3+2x^5-x^4+x^2+x-1\)
Sắp xếp : \(-1+x+x^2-x^3-x^4+2x^5\)
b ) Ta có :
\(P\left(x\right)=-5+x^2-4x^3+x^4-x^6\)
\(Q\left(x\right)=-1+x+x^2-x^3-x^4+2x^5\)
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\(P\left(x\right)+Q\left(x\right)=-6+x+2x^2-5x^3+2x^5-x^6\)
\(P\left(x\right)-Q\left(x\right)=4+x+3x^2-2x^4+2x^5+x^6\)
a) Lũy thừa tăng của biến:
\(P\left(x\right)=3x^2-5+x^4-3x^3-x^6-2x^2-x^3\)
\(=\left(3x^2-2x^2\right)+\left(-3x^3-x^3\right)+x^4-x^6-5\)
\(=x^2-4x^3+x^4-x^6-5\)
\(=-5+x^2-4x^3+x^4-x^6\)
\(Q\left(x\right)=x^3+2x^5-x^4+x^2-2x^3+x-1\)
\(=\left(x^3-2x^3\right)+2x^5-x^4+x^2+x-1\)
\(=-x^3+2x^5-x^4+x^2+x-1\)
\(=-1+x+x^2-x^3-x^4+2x^5\)
b) P(x)+Q(x)
\(P\left(x\right)+Q\left(x\right)=\left(-5+x^2-4x^3+x^4-x^6\right)+\left(-1+x+x^2-x^3-x^4+2x^5\right)\)
\(=\left(-5\right)+x^2-4x^3+x^4-x^6+\left(-1\right)+x+x^2-x^3-x^4+2x^5\)
\(=\left(-5-1\right)+x+\left(x^2+x^2\right)+\left(-4x^3-x^3\right)+\left(x^4-x^4\right)+2x^5-x^6\)
\(=-6+x+2x^2-5x^3+2x^5-x^6\)
\(P\left(x\right)-Q\left(x\right)=\left(-5+x^2-4x^3+x^4-x^6\right)-\left(-1+x+x^2-x^3-x^4+2x^5\right)\)
\(=\left(-5\right)+x^2-4x^3+x^4-x^6+1-x-x^2+x^3+x^4-2x^5\)
\(=\left(-5+1\right)+x+\left(x^2-x^2\right)+\left(-4x^3+x^3\right)+\left(x^4+x^4\right)-2x^5-x^6\)
\(=-4+x-3x^3+2x^4-2x^5-x^6\)
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a) P(x) = 3x2 - 5 + x4 - 3x3 - x6 - 2x2 - x3
= -5 + 3x2 - 2x2 + (-3x3 - x3) + x4 - x6
= -5 + x2 - 4x3 + x4 - x6
Q(x) = x3 + 2x5 - x4 + x2 - 2x3 + x - 1
= -1 + x + x2 + (x3 - 2x3) - x4 + 2x5
= -1 + x + x2 - x3 - x4 + 2x5
b) P(x) + Q(x) = -5 + x2 - 4x3 + x4 - x6 + (-1) + x + x2 - x3 - x4 + 2x5
= -x6 + 2x5 + x4 - x4 + (-4x3 - x3) + (x2 + x2) + x + [ -5 + (-1)]
= -x6 + 2x5 - 5x3 + 2x2 + x -6
P(x) - Q(x) = tự làm nhé
Ta có h(x) = f(x) - g(x)
= -x5 + 2x4 - x2 - 1 - (-6 + 2x + 3x3 - x4 - 3x5)
= 2x5 + 3x4 - 3x3 - x2 - 2x + 5
q(x) = g(x) - f(x) = -[f(x) - g(x)]
- h(x) = -2x5 - 3x4 + 3x3 + x2 + 2x - 5 (1)
Ta có h(1) = 2.15 + 3.14 - 3.13 - 12 - 2.1 + 5 = 4
h(-1) = 2(-1)5 + 3.(-1)4 - 3(-1)3 - (-1)2 - 2(-1) + 5
= 10
h(-2) = 2(-2)5 + 3.(-2)4 - 3(-2)3 - (-2)2 - 2(-2) + 5
= 17
h(2) = 2.25 + 3.24 - 3.23 - 22 - 2.2 + 5 = 85
Vì h(x) = -g(x)
=> g(1) = - 4 ; g(-1) = 10 ; g(2) = -85 ; g(-2) = 17
b)
Từ (1) => h(x) = -g(x)
a) \(M\left(x\right)=P\left(x\right)+Q\left(x\right)+2019\)
\(=-3x^5+x^2-1009+\frac{1}{2}x^4-8x^3+x-2x^3+3x^5+\frac{1}{2}x^4-1010+2019\)
\(=x^4-10x^3+x^2+x\)
b) \(K\left(x\right)=Q\left(x\right)-P\left(x\right)+1\)
\(=x-2x^3+3x^5+\frac{1}{2}x^4-1010+3x^5-x^2+1009-\frac{1}{2}x^4+8x^3+1\)
\(=6x^5+6x^3-x^2+x\)
M(x) = P(x) + Q(x) + 2019
= -3x5 + x2 - 1009 + 1/2x4 - 8x3 + x - 2x3 + 3x5 + 1/2x4 - 1010 + 2019
= ( 3x5 - 3x5 ) + ( 1/2x4 + 1/2x4 ) + ( 2x3 - 8x3 ) + x2 + x + ( -1010 - 1009 + 2019 )
= x4 - 6x3 + x2 + x
K(x) = Q(x) - P(x) + 1
= x - 2x3 + 3x5 + 1/2x4 - 1010 - ( -3x5 + x2 - 1009 + 1/2x4 - 8x3 ) + 1
= x - 2x3 + 3x5 + 1/2x4 - 1010 + 3x5 - x2 + 1009 - 1/2x4 + 8x3 + 1
= ( 3x5 + 3x5 ) + ( 1/2x4 - 1/2x4 ) + ( 8x3 - 2x3 ) - x2 + x + ( 1009 - 1010 + 1 )
= 6x5 + 6x3 - x2 + x