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a) x5-3x2+x4-\(\dfrac{1}{2}\)x-x5+5x4+x2-1
= (x5-x5)+(x4+5x4)+(x2-3x2)-\(\dfrac{1}{2}\)x-1
= 6x4-2x2-\(\dfrac{1}{2}\)x-1
b) x-x9+x2-5x3+x6-x+3x9+2x6-x3+7
= (3x9-x9)+(2x6+x6)-(5x3+x3)+x2+(x-x)+7
= 2x9+3x6-6x3+x2+7
a) \(A=\)\(x^4\)\(+4x^3\)\(+2x^2\)\(+x\)\(-7\)
\(B=\)\(2x^4\)\(-4x^3\)\(-2x^2\)\(-5x\)\(+3\)
b) f(x)= A(x)+B(x)= \(3x^4-4x\)\(-4\)
g(x)=A(x)-B(x) = \(-x^4+8x^3+4x^2+6x\)\(-10\)
c) g(x)= \(0^4+8.0^3+4.0^2\)\(+6.0\)\(-10\)
= -10
g(-2)=\(-2^4+8.-2^3+4.-2^2+6.-2\)\(-10\)
=\(-54\)
\(M\left(x\right)=P\left(x\right)+Q\left(x\right)=2,5x^6-4+2,5x^5-6x^3+2x^2\)-5x+\(3x-2,5x^6-x^2+5-2,5x^5+6x^3\)
=\(\left(2,5x^6-2,5x^6\right)\)+\(\left(2,5x^5-2,5x^5\right)\)\(\left(-6x^3+6x^3\right)\)+\(\left(2x^2-x^2\right)\)+\(\left(-5x+3x\right)\)+(-4+5)
= \(x^2-2x+1\)
\(P\left(x\right)+Q\left(x\right)=f\left(x\right)-g\left(x\right)\)
\(f\left(x\right)-g\left(x\right)=3x^4+3x^3-5x^2+x-5-x^4-3x^3+3x^2-5x+7\)
\(=2x^4-2x^2-4x+2\)
\(\Rightarrow P\left(x\right)+Q\left(x\right)=2x^4-2x^2-4x+2\left(1\right)\)
\(P\left(x\right)-Q\left(x\right)=g\left(x\right)+h\left(x\right)\)
\(g\left(x\right)+h\left(x\right)=x^4+3x^3-3x^2+5x-7+5x^4+2x^3+x^2-5\)
\(=6x^4+5x^3-2x^2+5x-12\)
\(\Rightarrow P\left(x\right)-Q\left(x\right)=6x^4+5x^3-2x^2+5x-12\left(2\right)\)
Từ ( 1 );( 2 ) thì tìm dc P(x) và Q(x)
a)
\(Q\left(x\right)=-1x^4+3x^2-5x^3-3-x\)
Sắp xếp: \(Q\left(x\right)=-1x^4-5x^3+3x^2-x-3\)
\(P\left(x\right)=5x^3+2x^2+1x^4+4+x\)
Sắp xếp: \(P\left(x\right)=1x^4+5x^3+2x^2+x+4\)
b)
\(Q\left(x\right)+P\left(x\right)=\left(-1x^4+3x^2-5x^3-x-3\right)+\left(1x^4+5x^3+2x^2+x+4\right)\)
\(=-1x^4-3x^2-5x^3-x-3+1x^4+5x^3+2x^2+x+4\)
\(=\left(-1x^4+1x^4\right)+\left(-3x^2+2x^2\right)+\left(-5x^3+5x^3\right)+\left(-x+x\right)+\left(-3+4\right)\)
\(=-1x^2+1\)
Vậy P(x) + Q(x) = -1x2 + 1
\(Q\left(x\right)+P\left(x\right)=\left(-1x^4+3x^2-5x^3-x-3\right)-\left(1x^4+5x^3+2x^2-x-4\right)\)
\(=-1x^4+3x^2-5x^3-x-3-1x^4-5x^3-2x^2-x-4\)
\(=\left(-1x^4-1x^4\right)+\left(3x^2-2x^2\right)+\left(-5x^3-5x^3\right)+\left(x-x\right)+\left(-3-4\right)\)
\(=-2x^4+x^2-10x^3-7\)
Vậy P(x) - Q(x) = -2x4 + x2 - 10x3 - 7
a)
Q\left(x\right)=-1x^4+3x^2-5x^3-3-xQ(x)=−1x4+3x2−5x3−3−x
Sắp xếp: Q\left(x\right)=-1x^4-5x^3+3x^2-x-3Q(x)=−1x4−5x3+3x2−x−3
P\left(x\right)=5x^3+2x^2+1x^4+4+xP(x)=5x3+2x2+1x4+4+x
Sắp xếp: P\left(x\right)=1x^4+5x^3+2x^2+x+4P(x)=1x4+5x3+2x2+x+4
b)
Q\left(x\right)+P\left(x\right)=\left(-1x^4+3x^2-5x^3-x-3\right)+\left(1x^4+5x^3+2x^2+x+4\right)Q(x)+P(x)=(−1x4+3x2−5x3−x−3)+(1x4+5x3+2x2+x+4)
=-1x^4-3x^2-5x^3-x-3+1x^4+5x^3+2x^2+x+4=−1x4−3x2−5x3−x−3+1x4+5x3+2x2+x+4
=\left(-1x^4+1x^4\right)+\left(-3x^2+2x^2\right)+\left(-5x^3+5x^3\right)+\left(-x+x\right)+\left(-3+4\right)=(−1x4+1x4)+(−3x2+2x2)+(−5x3+5x3)+(−x+x)+(−3+4)
=-1x^2+1=−1x2+1
Vậy P(x) + Q(x) = -1x2 + 1
Q\left(x\right)+P\left(x\right)=\left(-1x^4+3x^2-5x^3-x-3\right)-\left(1x^4+5x^3+2x^2-x-4\right)Q(x)+P(x)=(−1x4+3x2−5x3−x−3)−(1x4+5x3+2x2−x−4)
=-1x^4+3x^2-5x^3-x-3-1x^4-5x^3-2x^2-x-4=−1x4+3x2−5x3−x−3−1x4−5x3−2x2−x−4
=\left(-1x^4-1x^4\right)+\left(3x^2-2x^2\right)+\left(-5x^3-5x^3\right)+\left(x-x\right)+\left(-3-4\right)=(−1x4−1x4)+(3x2−2x2)+(−5x3−5x3)+(x−x)+(−3−4)
=-2x^4+x^2-10x^3-7=−2x4+x2−10x3−7
Vậy P(x) - Q(x) = -2x4 + x2 - 10x3 - 7