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x3 - 3x2 - 9x - 5 = (x3 - 5x2) + (2x2 -10x) + (x - 5) = x2 (x - 5) + 2x(x - 5) + (x - 5) = (x - 5)(x2 + 2x + 1) = (x - 5)(x + 1)2
x^3-3x^2-9x-5
=x^3-5x^2+2x^2-10x+x-5
=x^2(x-5)+2x(x-5)+(x-5)
=(x-5)(x^2+2x+1)
=(x-5)(x+1)^2
Nham nghiem thi ta thay pt co 1 ngiem x=2/3
=> tach nhu sau :
\(3x^3-2x^2-3x^2+2x+3x-2\)
\(3x^2\left(x-\frac{2}{3}\right)-3x\left(x-\frac{2}{3}\right)+3\left(x-\frac{2}{3}\right)\)
\(\left(x-\frac{2}{3}\right)\left(3x^2-3x+3\right)\)
Chuc ban hoc tot
1/(x+2)2 -(3x-1)2=(x+2+3x-1)(x+2-3x+1)=4x(-2x+3)=-8x2+12x
2/(x4+x2)(-2x3-2x)=x2(x2+1)-2x(x2+1)=(x2+1)(x2-2x)
\(3x^4-5x^3-18x^2-3x+5\)
\(=3x^4-6x^3+x^3-15x^2-2x^2-x^2-5x+2x+5\)\(=\left(3x^4-6x^3-15x^2\right)+\left(x^3-2x^2-5x\right)-\left(x^2-2x-5\right)\)
\(=3x^2\left(x^2-2x-5\right)+x\left(x^2-2x-5\right)-\left(x^2-2x-5\right)\)
\(=\left(3x^2+x-1\right)\left(x^2-2x-5\right)\)
\(x^2\left(x+1\right)-\left(x+1\right)\left(3x+1\right)+7x-x^2\)
\(=x^3+x^2-3x^2-4x-1+7x-x^2\)
\(=x^3-3x^2+3x-1\)
\(=\left(x-1\right)^3\)
Dấu nhân hay dấu cộng( trừ vậy bạn).
\(x^2+3x-4\)
\(=x^2+3x+\frac{9}{4}-\frac{25}{4}\)
\(=\left(x+\frac{3}{2}\right)^2-\left(\frac{5}{2}\right)^2\)
\(=\left(x+4\right)\left(x-1\right)\)