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a) \(A\left(x\right)=2x^4-5x^3-x^4-6x^2+5+5x^2-10+x\)
\(=\left(2x^4-x^4\right)-5x^3+\left(5x^2-6x^2\right)+x+\left(5-10\right)\)
\(=3x^4-5x^3-x^2+x-5\)
\(B\left(x\right)=-7-4x+6x^4+6+3x-x^3-3x^4\)
\(=\left(6x^4-3x^4\right)-x^3+\left(3x-4x\right)+\left(6-7\right)\)
\(=x^4-x^3-x-1\)
b) \(A\left(x\right)+B\left(x\right)\)
\(=\left(3x^4-5x^3-x^2+x-5\right)+\left(x^4-x^3-x-1\right)\)
\(=5x^4-6x^3-x^2-6\)
\(A\left(x\right)-B\left(x\right)\)
\(=\left(3x^4-5x^3-x^2+x-5\right)-\left(x^4-x^3-x-1\right)\)
\(=\left(3x^4-5x^3-x^2+x-5\right)-x^4+x^3+x+1\)
\(=2x^4-4x^3-x^2+2x-4\)
\(A=x^7-2x^4+3x^3-3x^4+2x^7-x+7-2x^3\)
\(A=3x^7-5x^4+x^3-x+7\)
\(B=3x^2-4x^4-3x^2-5x^5-0,5x-2x^2-3\)
\(B=-5x^5-4x^4-2x^2-0,5x-3\)
\(A+B=3x^7-5x^4+x^3-x+7-5x^5-4x^4-2x^2-0,5x-3\)
\(A+B=3x^7-9x^4+x^3-1,5x+4\)
\(A-B=3x^7-5x^4+x^3-x+7+5x^5+4x^4+2x^2+0,5x+3\)
\(A-B=3x^7-x^4+x^3-0,5x+10+5x^5\)
a)\(A\left(x\right)=5x^5-4x^4-2x^3+4x^2+3x+6\\ B\left(x\right)=x^5+2x^4-2x^3+3x^2-x+\frac{1}{4}\)
b)\(A\left(x\right)+B\left(x\right)\)
\(\left(5x^5-4x^4-2x^3+4x^2+3x+6\right)+\left(x^5+2x^4-2x^3+3x^2-x+\frac{1}{4}\right)\\ =5x^2-4x^4-2x^3+4x^2+3x+6+x^5+2x^4-2x^3+3x^2-x+\frac{1}{4}\\ =\left(5x^5+x^5\right)+\left(-4x^4+2x^4\right)+\left(-2x^3-2x^3\right)+\left(4x^2+3x^2\right)+\left(3x-x\right)+\left(6+\frac{1}{4}\right)\\ =6x^5-2x^4-4x^3+7x^2+2x+\frac{25}{4}\)
a) dễ tự làm
b) A(x) có bậc 6
hệ số: -1 ; 5 ; 6 ; 9 ; 4 ; 3
B(x) có bậc 6
hệ số: 2 ; -5 ; 3 ; 4 ; 7
c) bó tay
d) cx bó tay
Bài 1:
a)
\(F+G+H=(x^3-2x^2+3x+1)+(x^3+x-1)+(2x^2-1)\)
\(=2x^3+4x-1\)
b)
\(F-G+H=0\)
\(\Leftrightarrow (x^3-2x^2+3x+1)-(x^3+x-1)+(2x^2-1)=0\)
\(\Leftrightarrow 2x+1=0\)
\(\Leftrightarrow x=-\frac{1}{2}\)
Bài 2:
a)
\(A=-4x^5-x^3+4x^2-5x+9+4x^5-6x^2-2\)
\(=(-4x^5+4x^5)-x^3+(4x^2-6x^2)-5x+(9-2)\)
\(=-x^3-2x^2-5x+7\)
\(B=-3x^4-2x^3+10x^2-8x+5x^3\)
\(=-3x^4+(5x^3-2x^3)+10x^2-8x\)
\(=-3x^4+3x^3+10x^2-8x\)
b)
\(P=A+B=(-x^3-2x^2-5x+7)+(-3x^4+3x^3+10x^2-8x)\)
\(=-3x^4+(3x^3-x^3)+(10x^2-2x^2)-(8x+5x)+7\)
\(=-3x^4+2x^3+8x^2-13x+7\)
\(P(-1)=-3.(-1)^4+2(-1)^3+8(-1)^2-12(-1)+7=23\)
\(Q=A-B=(-x^3-2x^2-5x+7)-(-3x^4+3x^3+10x^2-8x)\)
\(=3x^4-(x^3+3x^3)-(2x^2+10x^2)+(8x-5x)+7\)
\(=3x^4-4x^3-12x^2+3x+7\)
Đù mỗi mình sai :v
Miyuki Misaki đen lắm