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a) Ta có: \(P\left(x\right)=5x^2-7+6x-8x^3-x^4\)
\(=-x^4-8x^3+5x^2+6x-7\)
Ta có: \(Q\left(x\right)=x^4+5+8x^3-5x^2\)
\(=x^4+8x^3-5x^2+5\)
b) Ta có: P(x)+Q(x)
\(=-x^4-8x^3+5x^2+6x-7+x^4+8x^3-5x^2+5\)
\(=6x-2\)
c) Ta có: P(x)-Q(x)
\(=-x^4-8x^3+5x^2+6x-7-\left(x^4+8x^3-5x^2+5\right)\)
\(=-x^4-8x^3+5x^2+6x-7-x^4-8x^3+5x^2-5\)
\(=-2x^4-16x^3+10x^2+6x-12\)
câu a dễ bạn tự làm nha
b) Ta có: P(x)+Q(x)
=−x4−8x3+5x2+6x−7+x4+8x3−5x2+5=−x4−8x3+5x2+6x−7+x4+8x3−5x2+5
=6x−2=6x−2
c) Ta có: P(x)-Q(x)
=−x4−8x3+5x2+6x−7−(x4+8x3−5x2+5)=−x4−8x3+5x2+6x−7−(x4+8x3−5x2+5)
=−x4−8x3+5x2+6x−7−x4−8x3+5x2−5=−x4−8x3+5x2+6x−7−x4−8x3+5x2−5
=−2x4−16x3+10x2+6x−12
a) Thu gọn và sắp xếp đa thức trên theo lũy thừa tăng dần của biến
* \(P\left(x\right)=3x^5-5x^5+x^4-2x-x^5+3x^4-x^2+x+1\)
\(P\left(x\right)=1+\left(-2x+x\right)+\left(-x^2\right)+\left(x^4+3x^4\right)+\left(3x^5-5x^5-x^5\right)\)
\(P\left(x\right)=1-x-x^2+4x^4-3x^5\)
* \(Q_x=-5+3x^5-2x+3x^2-x^5+2x-3x^3-3x^4\)
\(Q\left(x\right)=-5+\left(-2x+2x\right)+3x^2+\left(-3x^3\right)+\left(-3x^4\right)+\left(3x^5-x^5\right)\)
\(Q\left(x\right)=-5+3x^2-3x^3-3x^4+2x^5\)
b)
* \(P\left(x\right)+Q\left(x\right)=\left(3x^5-5x^2+x^4-2x-x^5+3x^4-x^2+x+1\right)+\left(-5+3x^5-2x+3x^2-x^5+2x-3x^3-3x^4\right)\)
\(P\left(x\right)+Q\left(x\right)=\left(1-x-x^2+4x^4-3x^5\right)+\left(-5+3x^2-3x^3-3x^4+2x^5\right)\)\(P\left(x\right)+Q\left(x\right)=\left(1+-5\right)+\left(-x^2+3x^2\right)+\left(4x^4-3x^4\right)+\left(-3x^5+2x^5\right)-x-3x^3\)
\(P\left(x\right)+Q\left(x\right)=-4-x+x^2-3x^3+x^4-x^5\)
* \(P\left(x\right)-Q\left(x\right)=\left(3x^5-5x^2+x^4-2x-x^5+3x^4-x^2+x+1\right)-\left(-5+3x^5-2x+3x^2-x^5+2x-3x^3-3x^4\right)\)
\(P\left(x\right)-Q\left(x\right)=\left(1-x-x^2+4x^4-3x^5\right)-\left(-5+3x^2-3x^3-3x^4+2x^5\right)\)
\(P\left(x\right)-Q\left(x\right)=1-x-x^2+4x^4-3x^5+5-3x^2+3x^3+3x^4-2x^5\)
\(P\left(x\right)-Q\left(x\right)=\left(1+5\right)+\left(-x^2-3x^2\right)+\left(4x^4+3x^4\right)+\left(-3x^5-2x^5\right)-x+3x^3\)
\(P\left(x\right)-Q\left(x\right)=6-4x+7x^4-5x^5-x+3x^3\)
\(P\left(x\right)=5x^2+3x-4-2x^3+4x^2-6\)
\(P\left(x\right)=\left(5x^2+4x^2\right)+3x+\left(-4-6\right)-2x^3\)
\(P\left(x\right)=9x^2+3x-10-2x^3\)
\(Q\left(x\right)=2x^4-x+3x^2-2x^3+\frac{1}{4}-x^5\)
\(Q\left(x\right)=2x^4-x+3x^2-2x^3+\frac{1}{4}-x^5\)
Sắp giảm :
\(P\left(x\right)=-2x^3+9x^2+3x-10\)
\(Q\left(x\right)=-x^5+2x^4-2x^3+3x^2-x+\frac{1}{4}\)
\(A\left(x\right)=P\left(x\right)+Q\left(x\right)\)
\(A\left(x\right)\)= \(\left[\left(-2x^3+9x^2+3x-10\right)-\left(-x^5+2x^4-2x^3+3x^2-x+\frac{1}{4}\right)\right]\)
\(A\left(x\right)=\)\(-2x^3+9x^2+3x-10+x^5-2x^4+2x^3-3x^2+x-\frac{1}{4}\)
\(A\left(x\right)=\)\(\left(-2x^3+2x^3\right)+\left(9x^2-3x^2\right)+\left(3x-x\right)+\left(-10-\frac{1}{4}\right)+x^5-2x^4\)
\(A\left(x\right)=6x^2+2x-2,75+x^5-2x^4\)
A(X)=2x2+2x-3x2+1
=-x2+2x+1
B(x)=2x2+3x3-x-5
=3x3+2x2-x-5
A(X)+B(x)=-x2+2x+1+3x3+2x2-x-5=3x3+x2+x-4
A(X)-B(x)=-x2+2x+1-3x3-2x2+x+5=-3x3-3x2+3x+6
Chọn đáp án D