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a, Sắp xếp : \(P\left(x\right)=2x^3+5x^2-3x^4+7-4x\)
\(\Rightarrow P\left(x\right)=-3x^4+2x^3-5x^2-4x+7\)
\(Q\left(x\right)=-3+2x^4-x+x^3-5x^2\)
\(\Rightarrow Q\left(x\right)=2x^4+x^3-5x^2-x-3\)
b, Ta có :* Đặt \(V\left(x\right)=P\left(x\right)+Q\left(x\right)\)
hay \(V\left(x\right)=2x^3+5x^2-3x^4+7-4x-3+2x^4-x+x^3-5x^2\)
\(=3x^3-x^4+4-5x\)
Vậy \(V\left(x\right)=3x^3-x^4+4-5x\)
Ta có : * Đặt \(K\left(x\right)=P\left(x\right)-Q\left(x\right)\)
hay \(2x^3+5x^2-3x^4+7-4x-\left(-3+2x^4-x+x^3-5x^2\right)\)
\(=2x^3+5x^2-3x^4+7-4x+3-2x^4+x-x^3+5x^2\)
\(=x^3+10x^2-5x^4+10-3x\)
Vậy \(K\left(x\right)=x^3+10x^2-5x^4+10-3x\)
a, P(x)= 5+x\(^3\)-2x+4x\(^3\)+3x\(^2\)-10
=(5-10) + (x\(^3\) + 4x\(^3\)) - 2x + 3x\(^2\)
= -5 + 5x\(^3\) - 2x + 3x\(^2\)
sắp xếp : P(x) = -5 - 2x + 3x\(^2\) + 5x\(^3\)
Q(x)=4-5x\(^3\)+2x\(^2\)-x\(^3\)+6x+11x\(^3\)-8x
= 4 - (5x\(^3\)-x\(^3\)+11x\(^3\)) + 2x\(^2\) + (6x - 8x)
= 4 - 15x\(^3\) + 2x\(^2\) - 2x
Sắp xếp : Q(x) = 4 - 2x + 2x\(^2\) -15 x\(^3\)
b, P(x) + Q(x) = ( -5-2x+3x\(^2\)+5x\(^3\)) + (4-2x+2x\(^2\)-15x\(^3\))
= -5 -2x + 3x\(^2\) + 5x\(^3\) + 4 - 2x + 2x\(^2\) - 15x\(^3\)
= (-5 + 4) + (-2x-2x) + (3x\(^2\)+ 2x\(^2\)) + (5x\(^3\) - 15x\(^3\))
=- 1 -4x+ 5x\(^2\) - 10x\(^3\)
P(x) - Q(x) = (-5-2x+3x\(^2\)+5x\(^3\)) - (4-2x+2x\(^2\)-15x\(^3\))
= -5-2x+3x\(^2\)+5x\(^3\)- 4+2x-2x\(^2\)+15x\(^3\)
= (-5-4) + (-2x+2x) + (3x\(^2\)-2x\(^2\)) + (5x\(^3\)+15x\(^3\))
= -9 + x\(^2\) + 20x\(^3\)
a) ta có Q=-2x^3+2x^2+12+5^-9x
Q=-2x^3+(2x^2+5x^2)-9x+12
Q=-2x^3+7x^2-9x+12
a, f(x) = -2x\(^3\) + 7 - 6x + 5x\(^4\) - 2x\(^3\)
=5x\(^4\)+(-2x\(^3\)-2x\(^3\))-6x+7
=5x\(^4\)-4x\(^3\)-6x+7
g(x)= 5x\(^2\) + 9x - 2x\(^4\) - x\(^2\)+ 4x\(^3\) -12
=-2x\(^4\)+4x\(^3\)+(5x\(^2\)-x\(^2\))+9x-12
=-2x\(^4\)+4x\(^3\)+4x\(^2\)+9x-12
b,f(x)+g(x)=5x\(^4\)-4x\(^3\)-6x+7+-2x\(^4\)+4x\(^3\)+4x\(^2\)+9x-12
=(5x\(^4\)-2x\(^4\))+(-4x\(^3\)+4x\(^3\))+4x\(^2\)+(-6x+9x)+(7-12)
= 3x\(^4\)+4x\(^2\)+3x-5
a: P(x)=4x-6x^3+5x-7x^2-9x+5
=-6x^3-7x^2+5
Q(x)=9x^3-3x^3+5x^2-4x^2+2x-2x-4
=6x^3+x^2-4
b: P(x)+Q(x)
=-6x^3-7x^2+5+6x^3+x^2-4
=-6x^2+1
P(x)-Q(x)
=-6x^3-7x^2+5-6x^3-x^2+4
=-12x^3-8x^2+9