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\(3x^4+6x^3-7x^2+8x-10\)
\(=\left(3x^4-3x^3\right)+\left(9x^3-9x^2\right)+\left(2x^2-2x\right)+\left(10x-10\right)\)
\(=\left(x-1\right)\left(3x^3+9x^2+2x+10\right)\)
Dễ mà ^_^: 3x2-7x+2=3x2 -x-6x+2=(3x2-x)-(6x-2)=x(3x-1)-2(3x-1)=(3x-1)(x-2)
3x3-7x2+17x-5
=3x3-x2-6x2+2x+15x-5
= x2.(3x-1)-2x.(3x-1)+5.(3x-1)
= (3x-1)(x2-2x+5)
Ta có : \(3x^3-7x^2+17x-5\)
\(=\left(3x^3-x^2\right)-\left(6x^2-2x\right)+\left(15x-5\right)\)
\(=x^2\left(3x-1\right)-2x\left(3x-1\right)+5\left(3x-1\right)\)
\(=\left(3x-1\right)\left(x^2-2x+5\right)\)
b) \(x^3-4x^2y+4xy^2-y^3\)
\(=x^3-3x^2y-x^2y+3xy^2+xy^2-y^3\)
\(=\left(x^3-3x^2y+3xy^2-y^3\right)-\left(x^2y-xy^2\right)\)
\(=\left(x-y\right)^3-xy\left(x-y\right)\)
\(=\left(x-y\right)\left[\left(x-y\right)^2-xy\right]\)
\(=\left(x-y\right)\left(x^2-2xy+y^2-xy\right)\)
\(=\left(x-y\right)\left(x^2-3xy+y^2\right)\)
\(3x^2+7x-6\)
\(=3x^2+9x-2x-6\)
\(=3x\left(x+3\right)-2\left(x+3\right)\)
\(=\left(3x-2\right)\left(x+3\right)\)
(x^2+3x+2)(x^2+7x+12)
=(x2+x+2x+2)(x2+3x+4x+12)
=[x.(x+1)+2.(x+1)][x.(x+3)+4.(x+3)]
=(x+1)(x+2)(x+3)(x+4)
\(3x^4+11x^3-7x^2-2x+1=\left(3x^4+12x^3-3x^2-3x\right)+\left(-x^3-4x^2+x+1\right)\)
\(=\left(3x-1\right)\left(x^3+4x^2-x-1\right)\)
\(=2x^4+6x^3-3x^3-9x^2-3x^2-9x+2x+6\)
\(=2x^3\left(x+3\right)-3x^2\left(x+3\right)-3x\left(x+3\right)+2\left(x+3\right)\)
\(=\left(x+3\right)\left(2x^3-4x^2+x^2-2x-x+2\right)=\left(x+3\right)\left(x-2\right)\left(2x^2+x-1\right)\)
\(=\left(x+3\right)\left(x-2\right)\left(2x^2+2x-x-1\right)=\left(x+3\right)\left(x-2\right)\left(x+1\right)\left(2x-1\right)\)
2x^4+3x^3-12x^2-7x+6 = (2x^4-x^3)+(4x^3-2x^2)-(10x^2-5x)-(12x-6)
= x^3.(2x-1)+2x^2.(2x-1)-5x.(2x-1)-6.(2x-1) = (2x-1).(x^3+2x^2-5x-6)
= (2x-1).[ (x^3+x^2)+(x^2+x)-(6x+6) ] = (2x-1).(x+1).(x^2+x-6) = (2x-1).(x-1).[(x^2-2x)+(3x-6)]
= (2x-1).(x+1).(x-2).(x+3)
k mk nha
\(3x^2-7x-10\)
\(=3x^2+3x-10x-10\)
\(=3x\left(x+1\right)-10\left(x+1\right)\)
\(=\left(x+1\right)\left(3x-10\right)\)
3x2 - 7x - 10 = 3x2 + 3x - 10x - 10 = 3x(x + 1) - 10(x + 1) = (3x - 10)(x + 1)