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a,A( x ) \(=\) 2x\(^3\) - 3x\(^2\) + 2x +1
B( x ) \(=\) 3x\(^3\) +2x\(^2\) - x - 5
b,A(x) + B(x) \(=\) 2x\(^3\) - 3x\(^2\) + 2x +1 + 3x\(^3\) +2x\(^2\) - x - 5
A(x) + B(x) \(=\) 5x\(^3\) - x\(^2\) + x - 4.
c,A(x) - B(x) \(=\) 2x\(^3\) - 3x\(^2\) + 2x +1 - 3x\(^3\) - 2x\(^2\) + x + 5
A(x) - B(x) \(=\) -x\(^3\) - 5x\(^2\) +3x +6
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) \(A\left(x\right)=-5x^3-2x^2+x+9x^3-2x^2-\left(x-1\right)\)
\(=\left(9x^3-5x^3\right)-\left(2x^2+2x^2\right)+\left(x-x\right)+1\)
\(=4x^3-4x^2+1\)
\(C\left(x\right)=x^3-2x\left(3x+1\right)-4\)
\(=x^3-6x^2-2x-4\)
b) \(A\left(x\right)+C\left(x\right)=4x^3-4x^2+1+x^3-6x^2-2x-4\)
\(=\left(4x^3+x^3\right)-\left(4x^2+6x^2\right)-2x+\left(1-4\right)\)
\(=5x^3-10x^2-2x-3\)
\(A\left(x\right)-C\left(x\right)=4x^3-4x^2+1-\left(x^3-6x^2-2x-4\right)\)
\(=4x^3-4x^2+1-x^3+6x^2+2x+4\)
\(=\left(4x^3-x^3\right)+\left(6x^2-4x^2\right)+2x+\left(1+4\right)\)
\(=3x^3+2x^2+2x+5\)
a, \(A\left(x\right)=-5x^3-2x^2+x+9x^3-2x^2-\left(x-1\right)\)
\(=4x^3-4x^2+x-x+1=4x^3-4x^2+1\)
\(C\left(x\right)=x^3-2x\left(3x+1\right)-4=x^3-6x^2-2x-4\)
b, \(A\left(x\right)+C\left(x\right)=5x^3-10x^2-2x-3\)
\(A\left(x\right)-C\left(x\right)=3x^3+2x^2+2x+5\)
\(A=x^7-2x^4+3x^3-3x^4+2x^7-x+7-2x^3\)
\(A=3x^7-5x^4+x^3-x+7\)
\(B=3x^2-4x^4-3x^2-5x^5-0,5x-2x^2-3\)
\(B=-5x^5-4x^4-2x^2-0,5x-3\)
\(A+B=3x^7-5x^4+x^3-x+7-5x^5-4x^4-2x^2-0,5x-3\)
\(A+B=3x^7-9x^4+x^3-1,5x+4\)
\(A-B=3x^7-5x^4+x^3-x+7+5x^5+4x^4+2x^2+0,5x+3\)
\(A-B=3x^7-x^4+x^3-0,5x+10+5x^5\)
a) A(x) = 2x4 - x3 + 2x5 - x + 1
= 2x5 + 2x4 - x3 - x + 1
Bậc : 5
Hệ số cao nhất : 6
Hệ số tự do : 1
B(x) = x3 - 4x2 - 2x5 + x - 3x4 + 2
= -2x5 - 3x4 + x3 - 4x2 + 2
Bậc : 5
Hệ số cao nhất : -2
Hệ số tự do : 2
a) Ta có : \(A\left(x\right)+B\left(x\right)\)
\(=2x^3+2x-3x^2+1+2x^2+3x^3-x-5\)
\(=\left(2x^3+3x^3\right)+\left(-3x^2+2x^2\right)+\left(2x-x\right)+\left(1-5\right)\)
\(=5x^3-x^2-x-4\)
b) Ta sẽ sắp xếp như sau :
\(A\left(x\right)=2x^3-3x^2+2x+1\)
\(B\left(x\right)=3x^3+2x^2-x-5\)
c) Ta có : \(A\left(x\right)-B\left(x\right)\)
\(=\left(2x^3+2x-3x^2+1\right)-\left(2x^2+3x^3-x-5\right)\)
\(=2x^3+2x-3x^2+1-2x^2-3x^3+x+5\)
\(=\left(2x^3-3x^3\right)+\left(-3x^2-2x^2\right)+\left(2x+x\right)+\left(1+5\right)\)
\(=-x^3-5x^2+3x+6\)