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\(x^8+x^7+1\)
\(=x^8+x^7+x^6-x^6+x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x-xx+1\)
\(=\left(x^8-x^6+x^5-x^3+x^2\right)\)
\(+\left(x^7-x^5+x^4-x^2+x\right)\)
\(+\left(x^6-x^4+x^3-x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)
\(A=\left(x^2+x\right)^2-14\left(x^2+x\right)+24\)
Đặt \(x^2+x=t\), ta có:
\(A=t^2-14t+24\)
\(=t^2-2t-12t+24\)
\(=t\left(t-2\right)-12\left(t-2\right)\)
\(=\left(t-2\right)\left(t-12\right)\)
\(=\left(x^2+x-2\right)\left(x^2+x-12\right)\)
\(B=\left(x^2+x\right)^2+4x^2+4x-12\)
\(=\left(x^2+x\right)^2+4\left(x^2+x\right)-12\)
Đặt \(x^2+x=t\), ta có:
\(B=t^2+4t-12\)
\(=t^2+6t-2t-12\)
\(=t\left(t+6\right)-2\left(t+6\right)\)
\(=\left(t+6\right)\left(t-2\right)\)
\(=\left(x^2+x+6\right)\left(x^2+x-2\right)\)
\(C=\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+1\)
\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)+1\)
Đặt \(x^2+5x+4=t\), ta có:
\(C=t\left(t+2\right)+1\)
\(=t^2+2t+1\)
\(=\left(t+1\right)^2\)
\(=\left(x^2+5x+4+1\right)^2\)
\(=\left(x^2+5x+5\right)^2\)
\(D=\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)+15\)
\(=\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\)
Đặt \(x^2+8x+7=t\), ta có:
\(D=t\left(t+8\right)+15\)
\(=t^2+8t+15\)
\(=t^2+3t+5t+15\)
\(=t\left(t+3\right)+5\left(t+3\right)\)
\(=\left(t+3\right)\left(t+5\right)\)
\(=\left(x^2+8x+7+3\right)\left(x^2+8x+7+5\right)\)
\(=\left(x^2+8x+10\right)\left(x^2+8x+12\right)\)
\(F=\left(x^2+x+1\right)\left(x^2+x+2\right)-12\)
Đặt \(x^2+x+1=t\), ta có:
\(F=t\left(t+1\right)-12\)
\(=t^2+t-12\)
\(=t^2+4t-3t-12\)
\(=t\left(t+4\right)-3\left(t+4\right)\)
\(=\left(t+4\right)\left(t-3\right)\)
\(=\left(x^2+x+1+4\right)\left(x^2+x+1-3\right)\)
\(=\left(x^2+x+5\right)\left(x^2+x-2\right)\)
\(E=x^4+2x^3+5x^2+4x-12\)
\(=x^4-x^3+3x^3-3x^2+8x^2-8x+12x-12\)
\(=x^3\left(x-1\right)+3x^2\left(x-1\right)+8x\left(x-1\right)+12\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3+3x^2+8x+12\right)\)
\(=\left(x-1\right)\left(x^3+2x^2+x^2+2x+6x+12\right)\)
\(=\left(x-1\right)\left[x^2\left(x+2\right)+x\left(x+2\right)+6\left(x+2\right)\right]\)
\(=\left(x-1\right)\left(x+2\right)\left(x^2+x+6\right)\)
phân tích đa thức thành nhân tử
a/4x-3x-1
b/x^7+x^5+1
c/x^3-x^2-4
d/3x^3-7x^2+17x-5
e/x^2+2xy+y^2-x-y-12
Phân tích các đa thức sau thành nhân tử ... c) 6x(x+y)^2+3x^2y(x+y). 2: .... x3 - 5x + 8x - 4=x2 . x -5x + 8x -22 = (x2 - 22) . (x -5x + 8x )=(x-2) . (x+2) . 4x. x3 - 9x2 ..... Phân tích các đa thức sau thành nhân tử : a,x^3+5x^2+8x+4 b, x^3-9x^2+6x+16 .
\(B=\left(x^2+x+1\right)\left(x^2+x+2\right)-12\)
\(\Leftrightarrow B=\left(x^2+x+\dfrac{3}{2}-\dfrac{1}{2}\right)\left(x^2+x+\dfrac{3}{2}+\dfrac{1}{2}\right)-12\)
\(\Leftrightarrow B=\left(x^2+x+\dfrac{3}{2}\right)^2-\dfrac{1}{4}-12\)
\(\Leftrightarrow B=\left(x^2+x+\dfrac{3}{2}\right)^2-\dfrac{49}{4}\)
\(\Leftrightarrow B=\left(x^2+x+\dfrac{3}{2}-\dfrac{7}{2}\right)\left(x^2+x+\dfrac{3}{2}+\dfrac{7}{2}\right)\)
\(\Leftrightarrow B=\left(x^2+x-2\right)\left(x^2+x+5\right)\)
\(C=x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1\)
\(\Leftrightarrow C=x\left(x+3\right)\left(x+1\right)\left(x+2\right)+1\)
\(\Leftrightarrow C=\left(x^2+3x\right)\left(x^2+x+2x+2\right)+1\)
\(\Leftrightarrow C=\left(x^2+3x\right)\left(x^2+3x+2\right)+1\)
\(\Leftrightarrow C=\left(x^2+3x+1-1\right)\left(x^2+3x+1+1\right)+1\)
\(\Leftrightarrow C=\left(x^2+3x+1\right)^2-1+1\)
\(\Leftrightarrow C=\left(x^2+3x+1\right)^2\)
\(D=\left(x-1\right)\left(x-3\right)\left(x-5\right)\left(x-7\right)-20\)
\(\Leftrightarrow D=\left(x-1\right)\left(x-7\right)\left(x-3\right)\left(x-5\right)-20\)
\(\Leftrightarrow D=\left(x^2-x-7x+7\right)\left(x^2-3x-5x+15\right)-20\)
\(\Leftrightarrow D=\left(x^2-8x+7\right)\left(x^2-8x+15\right)-20\)
\(\Leftrightarrow D=\left(x^2-8x+11-4\right)\left(x^2-8x+11+4\right)-20\)
\(\Leftrightarrow D=\left(x^2-8x+11\right)^2-16-20\)
\(\Leftrightarrow D=\left(x^2-8x+11\right)^2-36\)
\(\Leftrightarrow D=\left(x^2-8x+11-6\right)\left(x^2-8x+11+6\right)\)
\(\Leftrightarrow D=\left(x^2-8x+5\right)\left(x^2-8x+17\right)\)
:D