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a) P(x) = – x6 – x4 – 4x3 + 3x2+ 5
Q(x) = 2x5 – x4 – x3 + x – 1
b) P(x) + Q(x) = – x6 + 2x5– 2x4 – 5x3 + 3x2+ x + 4
P(x) – Q(x) = – x6 – 2x5 – 3x3 + 3x2– x + 6
a: \(P\left(x\right)=-2x^5+x^4+3x^3-x-\dfrac{1}{2}\)
\(Q\left(x\right)=\dfrac{-2}{3}x^5-x^4-2x^3+\dfrac{1}{2}x\)
b: \(P\left(x\right)+Q\left(x\right)=-2x^5+x^4+3x^3-x-\dfrac{1}{2}-\dfrac{2}{3}x^5-x^4-2x^3+\dfrac{1}{2}x\)
\(=\dfrac{-8}{3}x^5+x^3-\dfrac{1}{2}x-\dfrac{1}{2}\)
b: \(P\left(x\right)-Q\left(x\right)=-2x^5+x^4+3x^3-x-\dfrac{1}{2}+\dfrac{2}{3}x^5+x^4+2x^3-\dfrac{1}{2}x\)
\(=-\dfrac{4}{3}x^5+2x^4+5x^3-\dfrac{3}{2}x-\dfrac{1}{2}\)
Câu 1 :
\(\left(x-2\right)^2=x^2-4x+4\)
Câu 2:
\(2x^2\left(4x-5x^3\right)+10x^5-5x^3\)
\(=8x^3-10x^5+10x^5-5x^3\)
\(=3x^3\)
\(\left(x-2\right)\left(x^2-2x+4\right)+\left(x-4\right)\left(x-2\right)\)
\(=x^3-4x^2+8x-8+x^2-6x+8\)
\(=x^3-3x^2+2x\)
Còn lại tự làm nha dài lắm
x^3 - 3x^2 - 11x +5 x^2 + 2x -1 x - 5 x^3 + 2x^2 - x -5x^2 - 10x +5 -5x^2 - 10x + 5 0
4x^4 - 3x^3 - 5x^2 + 9x - 3 x^2 - 3 4x^2 - 3x + 7 4x^4 - 12x^2 -3x^3 + 7x^2 + 9x - 3 -3x^3 + 9x 7x^2 - 3 7x^2 - 21 18
Trả lời:
a) P = ( 2x + 1 )2 - 4x6 - 2x5
= 4x2 + 4x + 1 - 4x6 - 2x5
= - 4x6 - 2x5 + 4x2 + 4x + 1
b) Q = ( x + 2 )5 - x5 - x4
= ( x + 2 )2( x + 2 )2( x + 2 ) - x5 - x4
= ( x2 + 4x + 4 )( x2 + 4x + 4 )( x + 2 ) - x5 - x4
= ( x4 + 4x3 + 4x2 + 4x3 + 16x2 + 16x + 4x2 + 16x + 16 )( x + 2 ) - x5 - x4
= ( x4 + 8x3 + 24x2 + 32x + 16 )( x + 2 ) - x5 - x4
= x5 + 2x4 + 8x4 + 16x3 + 24x3 + 48x2 + 32x2 + 64x + 16x + 32 - x5 - x4
= 9x4 + 40x3 + 80x2 + 80x + 32