Question

Phân tích các đa thức sau thành nhân tử:

* \(x^3-7x+6\)

* \(x^3-9x^2+6x+16\)

* \(x^3-6x^2-x+30\)

* \(2x^3-x^2+5x+3\)

* \(27x^3-27x^2+18x-4\)

* \(x^2+2xy+y^2-x-y-12\)

* \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

* \(4x^4-32x^2+1\)

* \(3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)^2\)

* \(64x^4+y^4\)

* \(a^6+a^4+a^2b^2+b^4-b^6\)

* \(x^3+3xy+y^3-1\)

* \(4x^4+4x^3+5x^2+2x+1\)

* \(x^8+x+1\)

* \(x^8+3x^4+4\)

* \(3x^2+22xy+11x+37y+7y^2+10\)

* \(x^4-8x+63\)

* \(\left(x+y+z\right)\left(xy+yz+zx\right)-xyz\)

* \(xy\left(x+y\right)-yz\left(y+z\right)+xz\left(x-z\right)\)

* \(\left(a+b\right)\left(a^2-b^2\right)+\left(b+c\right)\left(b^2-c^2\right)+\left(c+a\right)\left(c^2-a^2\right)\)

* \(a^4\left(b-c\right)+b^4\left(c-a\right)+c^4\left(a-b\right)\)

* \(a^3+b^3+c^3-3abc=\left(a+b\right)^3-3ab^2+c^3-3abc\)

* \(\left(a+b+c\right)^3-a^3-b^3-c^3=[\left(a+b\right)c]^3-a^3-b^3-c^3\)

* \(\left(x-y\right)^3+\left(y-z\right)^3+\left(z-x\right)^3\)

\([\) Các bạn làm được bài nài thì làm giúp mk với nha,làm vài câu cũng được\(]\)

Mk mệt quá rồi làm giúp mk với nha

Answer 1

\(1,x^3-7x+6\)

\(=x^3+3x^2-3x^2-9x+2x+6\)

\(=x^2\left(x+3\right)-3x\left(x+3\right)+2\left(x+3\right)\)

\(=\left(x+3\right)\left(x^2-3x+2\right)\)

\(=\left(x+3\right)\left(x^2-2x-x+2\right)\)

\(=\left(x+3\right)\left(x-2\right)\left(x-1\right)\)

\(2,x^3-9x^2+6x+16\)

\(=x^3+x^2-10x^2-10x+16x+16\)

\(=x^2\left(x+1\right)-10x\left(x+1\right)+16\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2-10x+16\right)\)

\(=\left(x+1\right)\left(x^2-2x-8x+16\right)\)

\(=\left(x+1\right)\left(x-8\right)\left(x-2\right)\)

Answer 2

mk ms lm hai câu thôi mà đã mệt r , bh mk lm bt mai đi học ,lúc khác lm đ cko bn

Answer 3

* $x^3-6x^2-x+30$

$\mathrm{=\; x3\; +2x2-8x2-16x+15x+30}$

$\mathrm{=(x3+2x2)-(8x2+16x)+(15x+30)}$

$\mathrm{=x2(x+2)-8x(x+2)+15(x+2)}$

$\mathrm{=\; (x+2)(x2-8x+15)}$

$\mathrm{=(x+2)(x2-3x-5x+15)}$

$\mathrm{=(x+2)[x(x-3)-5(x-3)]}$

$\mathrm{=\; (x+2)(x-5)(x-3)}$