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\(x^3+6x^2+11x+6=x^3+x^2+5x^2+5x+6x+6\)
\(=x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)=\left(x+1\right)\left(x^2+5x+6\right)\)
\(=\left(x+1\right)\left(x^2+2x+3x+6\right)=\left(x+1\right)\left[x\left(x+2\right)+3\left(x+2\right)\right]\)
\(=\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
Mai cho bn đấy tui dg định off =))
a)\(11x+11y-x^2-xy\)
\(=\left(11x+11y\right)-\left(x^2+xy\right)\)
\(=11\left(x+y\right)-x\left(x+y\right)\)
\(=\left(11-x\right)\left(x+y\right)\)
b)\(x^2-xy-8x+8y\)
\(=\left(x^2-xy\right)-\left(8x-8y\right)\)
\(=x\left(x-y\right)-8\left(x-y\right)\)
\(=\left(x-8\right)\left(x-y\right)\)
c)\(x^2-6x-y^2+9\)
\(=\left(x^2-6x+9\right)-y^2\)
\(=\left(x-3\right)^2-y^2=\left(x-3+y\right)\left(x-3-y\right)\)
d)\(x^2+2xy+y^2-xz-yz\)
\(=\left(x^2+2xy+y^2\right)-\left(xz+yz\right)\)
\(=\left(x+y\right)^2-z\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y-z\right)\)
a) \(11x+11y-x^2-xy\)
\(=11\left(x+y\right)-x\left(x+y\right)\)
\(=\left(x+y\right)\left(11-x\right)\)
b) \(x^2-xy-8x+8y\)
\(=x\left(x-y\right)-8\left(x-y\right)\)
\(=\left(x-y\right)\left(x-8\right)\)
c) \(x^2-6x-y^2+9\)
\(=\left(x^2-6x+9\right)-y^2\)
\(=\left(x-3\right)^2-y^2\)
\(=\left(x-3-y\right)\left(x-3+y\right)\)
d) \(x^2+2xy+y^2-xz-yz\)
\(=\left(x+y\right)^2-z\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y-z\right)\)
x^3 + 6x^2 + 11x + 6
= x^3 + x^2 + 5x^2 + 5x + 6x + 6
= x^2(x + 1) + 5x(x + 1) + 6(x + 1)
= (x + 1)(x^2 + 5x + 6)
= (x + 1)(x^2 + 2x + 3x + 6)
= (x + 1)[x(x + 2) + 3(x + 2)
= (x + 1)(x + 2)(x + 3)
a, \(x^4+6x^3+7x^2-6x+1\)
\(=x^4-2x^2+1+6x^3+9x^2+6x\)
\(=\left(x^2-1\right)^2+6x\left(x^2-1\right)+9x^2\)
\(=\left(x^2-1+3x\right)^2\)
b, \(x^4-7x^3+14x^2-7x+1\)
\(=x^4+2x^2+1+7x^3+12x^2-7x\)
\(=\left(x^2+1\right)^2-7x\left(x^2+1\right)+12^2\)
\(=\left(x^2-1+3x\right)^2\)
c, \(12x^2-11x-36\)
\(=12x^2-27x+16x-36\)
\(=3x\left(4x-9\right)+4\left(4x-9\right)\)
\(=\left(4x-9\right)\left(3x+4\right)\)
a, \(x^3+4x^2-29x+24\)
\(=x^3-x^2+5x^2-5x-24x+24\)
\(=x^2\left(x-1\right)+5x\left(x-1\right)-24\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+5x-24\right)\)
\(=\left(x-1\right)\left[x\left(x-3\right)+8\left(x-3\right)\right]\)
\(=\left(x-1\right)\left(x-3\right)\left(x+8\right)\)
\(x^3+6x^2+11x+6\)
\(=x^3+x^2+5x^2+5x+6x+6\)
\(=x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+5x+6\right)\)
\(=\left(x+1\right)\left[x\left(x+2\right)+3\left(x+2\right)\right]\)
\(=\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
Chúc bạn học tốt.
câu c:x^4-2x^3-x^2+x^3-2x^2-x+5x^2-10x-5=x^2(x^2-2x-1)+x(x^2-2x-1)+5(x^2-2x-1)=(x^2-2x-1)(x^2+x+5)
a)
\(x^3+6x^2+11x+6=(x^3-x)+(6x^2+12x+6)\)
\(=x(x^2-1)+5(x^2+2x+1)\)
\(=x(x-1)(x+1)+6(x+1)^2\)
\(=(x+1)[x(x-1)+6(x+1)]=(x+1)(x^2+5x+6)\)
\(=(x+1)(x^2+2x+3x+6)\)
\(=(x+1)[x(x+2)+3(x+2)]=(x+1)(x+2)(x+3)\)
b) \(x^3+6x^2-13x-42\)
\(=x^3+2x^2+4x^2+8x-21x-42\)
\(=x^2(x+2)+4x(x+2)-21(x+2)\)
\(=(x+2)(x^2+4x-21)\)
\(=(x+2)[x^2-3x+7x-21)\)
\(=(x+2)(x+7)(x-3)\)
c)
\(x^3-5x^2+8x-4=(x^3-x^2)-4x^2+8x-4\)
\(=x^2(x-1)-4(x^2-2x+1)\)
\(=x^2(x-1)-4(x-1)^2\)
\(=(x-1)[x^2-4(x-1)]=(x-1)(x^2-4x+4)\)
\(=(x-1)(x-2)^2\)
d) \(2x^3-x^2+3x+6\)
\(=2x^3+2x^2-3x^2+3x+6\)
\(=2x^2(x+1)-3(x^2-x-2)\)
\(=2x^2(x+1)-3[x^2+x-2x-2]\)
\(=2x^2(x+1)-3[x(x+1)-2(x+1)]\)
\(=2x^2(x+1)-3(x+1)(x-2)\)
\(=(x+1)(2x^2-3x+6)\)
a, \(6x^2-xy-y^2\)
\(=6x^2-3xy+2xy-y^2\)
\(=3x\left(2x-y\right)+2y\left(x-y\right)\)
\(=\left(3x+2y\right)\left(x-y\right)\)
b, \(8x^2-23x-3\)
\(=8x^2-24x+x-3\)
\(=8x\left(x-3\right)+\left(x-3\right)=\left(8x+1\right)\left(x-3\right)\)
c, \(10x^2-11x-6\)
\(=10x^2-15x+4x-6\)
\(=5x\left(2x-3\right)+2\left(2x-3\right)\)
\(=\left(5x+2\right)\left(2x-3\right)\)
d, \(x^3-6x^2+11x-6\)
\(=x^3-3x^2-3x^2+9x+2x-6\)
\(=x^2\left(x-3\right)-3x\left(x-3\right)+2\left(x-3\right)\)
\(=\left(x^2-3x+2\right)\left(x-3\right)\)
\(=\left(x^2-2x-x+2\right)\left(x-3\right)\)
\(=\left(x-1\right)\left(x-2\right)\left(x-3\right)\)