Question

Cho P(x) = x\(^2+5x^4-3x^3+x^2+4x^4+3x^3-x+5\)
Q(x)= x - 5x\(^3\)\(-x^2-x^4+4x^3-x^2+3x-1\)
a, Thu gọn, sắp xếp theo lũy thừa giảm của P(x)
b, Tính P(x) + Q(x); P(x) - Q(x)

Answer 1

a/ Thu gọn và sắp xếp:

\(P\left(x\right)=x^2+5x^4-3x^3+x^2+4x^4+3x^3-x+5=\left(5x^4+4x^4\right)+\left(3x^3-3x^3\right)+\left(x^2+x^2\right)-x+5=9x^4+2x^2-x+5\)

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\(Q\left(x\right)=x-5x^3-x^2-x^4+4x^3-x^2+3x-1=-x^4+\left(4x^3-5x^3\right)+\left(-x^2-x^2\right)+\left(x+3x\right)-1=-x^4-x^3-2x^2+4x-1\)

b/ \(P\left(x\right)+Q\left(x\right)=9x^4+2x^2-x+5+\left(-x^4-x^3-2x^2+4x-1\right)=9x^4+2x^2-x+5-x^4-x^3-2x^2+4x-1=8x^4-x^3+3x+4\)

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\(P\left(x\right)-Q\left(x\right)=9x^4+2x^2-x+5-\left(-x^4-x^3-2x^2+4x-1\right)=9x^4+2x^2-x+5+x^4+x^3+2x^2-4x+1=10x^4+x^3+4x^2-5x+6\)