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a) \(14x^3y:10x^2=\dfrac{7}{5}xy\)
b) \(\left(x^3-27\right):\left(3-x\right)\)
\(=\left(x-3\right)\left(x^2+3x+9\right):\left(3-x\right)\)
\(=-\left(3-x\right)\left(x^2+3x+9\right):\left(3-x\right)\)
\(=-\left(x^2+3x+9\right)\)
\(=-x^2-3x-9\)
a) 14x3y:10x2=\(\dfrac{7}{5}\)xy
b) (x3−27):(3−x)
=(x−3)(x2+3x+9):(3−x)
=−(3−x)(x2+3x+9):(3−x)
=−(x2+3x+9)=
=−x2−3x−9
\(=\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)\)
\(=\left(x+3\right)\left(x^2-3x+9+x-9\right)
\)
\(=\left(x+3\right)\left(x^2-2x\right)\)
\(7,\\ a,A=x^2-4x+3+11=\left(x-2\right)^2+10\ge10\\ \text{Dấu }"="\Leftrightarrow x=2\\ b,B=-\left(4x^2-4x+1\right)+6=-\left(2x-1\right)^2+6\le6\\ \text{Dấu }"="\Leftrightarrow x=\dfrac{1}{2}\\ c,x-y=2\Leftrightarrow x=y+2\\ \Leftrightarrow B=y^2-3x^2=y^2-3\left(y+2\right)^2\\ \Leftrightarrow B=y^2-3y^2-12y-12=-4y^2-12y-12\\ \Leftrightarrow B=-\left(4y^2+12y+9\right)-3=-\left(2y+3\right)^2-3\le-3\\ \text{Dấu }"="\Leftrightarrow y=-\dfrac{3}{2}\Leftrightarrow x=\dfrac{1}{2}\)
\(8,\\ \Leftrightarrow x^3-3x^2+5x+a=\left(x-2\right)\cdot a\left(x\right)\)
Thay \(x=2\Leftrightarrow8-12+10+a=0\Leftrightarrow a=-6\)
e) x3-3x2-4x+12
= x2(x-3)-4(x-3)
= (x2-4)(x-3)