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\(2x^4+x^3-6x^2+x+2\)
= \(2x^4+4x^3-3x^3-6x^2+x+2\)
= \(2x^3\left(x+2\right)-3x^2\left(x+2\right)+\left(x+2\right)\)
= \(\left(x+2\right)\left(2x^3-3x^2+1\right)\)
=\(\left(x+2\right)\left(2x^3-2x^2-x^2+1\right)\)
=\(\left(x+2\right)\left(2x^2\left(x-1\right)-\left(x+1\right)\left(x-1\right)\right)\)
=\(\left(x+2\right)\left(x-1\right)\left(2x^2-x-1\right)\)
= \(\left(x+2\right)\left(x-1\right)\left(2x^2-2x+x-1\right)\)
=\(\left(x+2\right)\left(x-1\right)\left(2x\left(x-1\right)+\left(x-1\right)\right)\)
=\(\left(x+2\right)\left(2x+1\right)\left(x-1\right)^2\)
a) x3-2x2-x+2
=x(x2-1)+2(-x2+1)
=x(x2-1)-2(x2-1)
=(x2-1)(x-2)
b)
x2+6x-y2+9
=x2+6x+9-y2
=(x+3)2-y2
=(x+3-y)(x+3+y)
a) xy+3x-7y-21
=x(y+3)-7(x+3)
=(x-7)(y+3)
b)2xy-15-6x-5y
=2x(y-3)-5(-3+y)
=(2x-5)(y-3)
c)2x^2y+2xy^2-2x-2y
=2x(xy-1)+2y(xy-1)
=(2x+2y)(xy-1)
x(x+3)-5x(x-5)-5(x+3)
=(x-5)(x+3)-5x(x-5)
=(x-5)(x+3-5x)
Câu cuối mình bị nhầm dòng cuối phải là (x-5)(x+3+x-5)=(x-5)(2x-2)nha bạn
\(=x^4-x^3+3x^3-3x^2+3x^2-3x+9x-9\\ =\left(x-1\right)\left(x^3+3x^2+3x+9\right)\\ =\left(x-1\right)\left(x+3\right)\left(x^2+3\right)\)
\(x^4+2x^3+6x-9=x^3\left(x-1\right)+3x^2\left(x-1\right)+3x\left(x-1\right)+9\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3+3x^2+3x+9\right)\)
\(=\left(x-1\right)\left[x^2\left(x+3\right)+3\left(x+3\right)\right]\)
\(=\left(x-1\right)\left(x+3\right)\left(x^2+3\right)\)
x3 + 2x2 - 6x - 27
= (x3 - 3x2) + (5x2 - 15x) + (9x - 27)
= x2(x - 3) + 5x(x - 3) + 9(x - 3)
= (x - 3)(x2 + 5x + 9)
1.
= (x^3 + 125 ) -(x^2 +5x)
=(x +5) (x^2 -5x +25) -x(x+5)
=(x+5)(x^2 -5x +25 -x)
=(x+5)(x^2 -6x +25)
2.
= (x^3 -27) + (2x^2 -6x)
=(x-3) (x^2 +3x +9) +2x (x-3)
=(x-3) (x^2 +3x +9 +2x)
=(x-3) (x^2 +5x +9)
1. \(x^3+2x^2-6x-27=\left(x-3\right)\left(x^2+5x+9\right)\)
2. \(9x^2+6x-4y^2-4y=\left(9x^2-4y^2\right)+\left(6x-4y\right)\)
\(=\left(3x-2y\right)\left(3x+2y\right)+2\left(3x-2y\right)=\left(3x-2y\right)\left(3x+2y+2\right)\)
3. \(12x^3+4x^2-27x-9=4x^2\left(3x+1\right)-9\left(3x+1\right)\)
\(=\left(3x+1\right)\left(x^2-\dfrac{9}{4}\right)=\left(x+\dfrac{1}{3}\right)\left(x+\dfrac{3}{2}\right)\left(x-\dfrac{3}{2}\right)\)
1) Ta có: \(x^3+2x^2-6x-27\)
\(=\left(x-3\right)\left(x^2+3x+9\right)+2x\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2+5x+9\right)\)
2: Ta có: \(9x^2+6x-4y^2-4y\)
\(=\left(3x-2y\right)\left(3x+2y\right)+2\left(3x-2y\right)\)
\(=\left(3x-2y\right)\left(3x+2y+2\right)\)
2x^5-6x^4-2a^2x^3-6ax^3
=(2x^5-2a^2x^3)-(6x^4+6ax^3)
=2x^3(x^2-a^2)-6x^3(x+a)
=2x^3(x-a)(x+a)-6x^3(x+a)
=(x+a)(2x^4-2x^3a-6x^3)
=(x+a) 2x^3 (x-a-3)
\(=x\left(2x^2-x-6\right)\)
\(=x\left(2x^2-4x+3x-6\right)\)
\(=x\left[2x\left(x-2\right)+3\left(x-2\right)\right]\)
\(=x\left(x-2\right)\left(2x+3\right)\)
x(2x^2-x-6)
x(2x^2-4x+3x-6)
x[2x(x-2)+3(x-2)]
x(2x+3)(x-2)