làm tính chia:
a)( x^2 +3x -2):(x-1)
b) (3x^2-3x+1):(x+2)
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a) (x + 2)(x2 + 3x + 1)
= x.x2 + x.3x + x.1 + 2.x2 + 2.3x + 2.1
= x3 + 3x2 + x + 2x2 + 6x + 2
= x3 + 5x2 + 7x + 2
b) (2x3 + 10x2 + 9x + 4) : (x + 4)
= (2x3 + 8x2 + 2x2 + 8x + x + 4) : (x + 4)
= [(2x3 + 8x2) + (2x2 + 8x) + (x + 4)] : (x + 4)
= [2x2(x + 4) + 2x(x + 4) + (x + 4)] : (x + 4)
= (x + 4)(2x2 + 2x + 1) : (x + 4)
= 2x2 + 2x + 1
a)\(\left(x+y\right)^2:\left(x+y\right)=x+y\)
b)\(\left(x-y\right)^5:\left(y-x\right)^4=\left(x-y\right)^5:\left(x-y\right)^4=x-y\)
c)\(\left(5x^4-3x^3+x^2\right):3x^2=\frac{5}{3}x^2-x+\frac{1}{3}^{ }\)
d)\(\left(x^3y^3-\frac{1}{2}x^2y^3+x^3y^2\right):\frac{1}{2}x^2y^2=2xy-y+x\)
\(\frac{x^4+x^3+6x^2+5x+5}{x^2+x+1}=\frac{x^4+x^3+x^2+5x^2+5x+5}{x^2+x+1}=\frac{x^2\left(x^2+x+1\right)+5\left(x^2+x+1\right)}{\left(x^2+x+1\right)}=\frac{\left(x^2+x+1\right)\left(x^2+5\right)}{x^2+x+1}=x^2+5\)
\(\frac{x^4+x^3+2x^2+x+1}{x^2+x+1}=\frac{x^4+x^3+x^2+x^2+x+1}{x^2+x+1}=\frac{x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)}{x^2+x+1}=\frac{\left(x^2+x+1\right)\left(x^2+1\right)}{x^2+x+1}=x^2+1\)