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6x3 - 11x2 - x - 2
= 6x3 - 12x2 + x2 - 2x + x - 2
= ( 6x3 - 12x2 ) + ( x2 - 2x ) + ( x - 2 )
= 6x2( x - 2 ) + x( x - 2 ) + 1( x - 2 )
= ( x - 2 )( 6x2 + x + 1 )
x3+6x2+11x+6 = x3+6x2+12x-x+8-2 = (x3+6x2+12x+8) - (x+2) = (x+2)3 - (x+2) = (x+2)[(x+2)2 - 1] = (x+2)(x+2-1)(x+2+1) = (x+2)(x+1)(x+3)
\(=x^2-2x-9x+18\)
\(=\left(x-2\right)\left(x-9\right)\)
OK k nha
Ta có:\(x^3+9x^2+11x-21\)
\(=x^3-x^2+10x^2-10x+21x-21=x^2\left(x-1\right)+10x\left(x-1\right)+21\left(x-1\right)\)
\(=\left(x^2+10x+21\right)\left(x-1\right)=\left(x^2+3x+7x+21\right)\left(x-1\right)\)
\(=\left[x\left(x+3\right)+7\left(x+3\right)\right]\left(x-1\right)\)
\(=\left(x+3\right)\left(x+7\right)\left(x-1\right)\)
x^3+9x^2+11x-21=x^3-x^2+10x^2-10x+21x-21=(x^3-x^2)+(10x^2-10x)+(21x-21)
=x^2(x-1)+10x(x-1)+21(x-1)=(x-1)(x^2+10x+21)=(x-1)(x^2+3x+7x+21)=(x-1)[(x^2+3x)+(7x+21)]
=(x-1)(x+7)(x+3)
x3 - 11x2 + 30x = x(x2 - 11x + 30) = x(x2 - 6x - 5x + 30) = x[x(x - 6) - 5(x - 6)] = x(x - 5)(x - 6)
\(x^2-11x+2\)
\(\text{Sử dụng biệt thức( cách này lớp 9 kì 2 hok nha)}\)
\(\text{denta}=b^2-4ac=11^2-2.1.4=113>0\)
=> pt có 2 No là:
\(x_1=\frac{11+\sqrt{113}}{2};x_2=\frac{11-\sqrt{113}}{2}\)
\(x^2-11x+2\)
\(=\left[x^2-2.x.\frac{11}{2}+\left(\frac{11}{2}\right)^2\right]-\frac{7}{2}\)
\(=\left(x-\frac{11}{2}\right)^2-\left(\sqrt{\frac{7}{2}}\right)^2\)
\(=\left(x-\frac{11}{2}+\sqrt{\frac{7}{2}}\right)\left(x-\frac{11}{2}-\sqrt{\frac{7}{2}}\right)\)
\(=\left(x-\frac{11}{2}+\frac{\sqrt{14}}{2}\right)\left(x-\frac{11}{2}-\frac{\sqrt{14}}{2}\right)\)
\(=\left(x+\frac{\sqrt{14}-11}{2}\right)\left(x-\frac{\sqrt{14}+11}{2}\right)\)
Tham khảo nhé~
\(x^3+6x^2+11x+6=\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
sai đề à bạn
ko đâu bạn ơi