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\(x^5+x^4+2\)
\(=x^5+x^4+x^2-x^2+1+1\)
\(=\left(x^5-x^2\right)+\left(x^4+x^2+1\right)\)
\(=\left(x^5-x^2\right)+\left(x^4+2x^2-x^2+1\right)+1\)
\(=x^2\left(x^3-1\right)+\left(x^4+2x^2-x^2+1\right)+1\)
\(=x^2\left(x-1\right)\left(x^2+x+1\right)+\left(\left(x^2+1\right)^2-x^2\right)+1\)
\(=x^2\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+1+x\right)\cdot\left(x^2+1-x\right)+1\)
\(=\left(x^3-x^2\right)\left(x^2+x+1\right)+\left(x^2+1+x\right)\cdot\left(x^2+1-x\right)+1\)
\(=\left(x^2+x+1\right)\left(x^3-x^2+x^2+1-x\right)+1\)
\(=\left(x^2+x+1\right)\left(x^3+1-x\right)+1\)
Nghịch xíu :v
a, \(x^3-2x-4\)
\(=x^3-2x^2+2x^2-4x+2x-4\)
\(=x^2\left(x-2\right)-2x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2-2x+2\right)\)
b, \(x^2+4x+3\)
\(=x^2+x+3x+3=x\left(x+1\right)+3\left(x+1\right)\)
\(=\left(x+1\right)\left(x+3\right)\)
Chúc bạn học tốt!!!
Trả lời:
a) \(x^3+2x=x\left(x^2+2\right)\)
b) \(3x^3-12x^2=3x^2\left(x-4\right)\)
\(2,25x^2-12x-13\)
\(=25x^2-25x+13x-13\)
\(=25x\left(x-1\right)+13\left(x-1\right)\)
\(=\left(x-1\right)\left(25x+13\right)\)
\(3,2y^2-3y-5\)
\(=2y^2+2y-5y-5\)
\(=2y\left(y+1\right)-5\left(y+1\right)\)
\(=\left(y+1\right)\left(2y-5\right)\)
Còn bài 1 mik đang nghĩ, khi nào biết mik trả lời nha!!!
Chúc bn học giỏi!!!
Bai 1
\(x^2+x-30=x^2+6x-5x-30=\left(x-5\right)\left(x+6\right)\)
Bai 2
a, \(\left(x-2\right)^2-x\left(x-5\right)=13\)
\(\Leftrightarrow x^2-4x+4-x^2+5x=13\)
\(\Leftrightarrow x+4=13\Leftrightarrow x=9\)
b, \(4x^3-100x=0\Leftrightarrow x\left(4x^2-100\right)=0\)
\(\Leftrightarrow x\left(2x-10\right)\left(2x+10\right)=0\Leftrightarrow x=0;\pm5\)
\(x^2-\frac{5}{3}x-\frac{2}{3}\)
\(=x^2-2x+\frac{1}{3}x-\frac{2}{3}\)
\(=x\left(x-2\right)+\frac{1}{3}\left(x-2\right)\)
\(=\left(x-2\right)\left(x+\frac{1}{3}\right)\)
\(x^3-5x^2-14x\)
\(=x^3+2x^2-7x^2-14x\)
\(=x^2\left(x+2\right)-7x\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-7x\right)\)
\(=x\left(x+2\right)\left(x-7\right)\)
\(x^3-7x-6\)
\(=x^3+x^2-x^2-x-6x-6\)
\(=x^2\left(x+1\right)-x\left(x+1\right)-6\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x-6\right)\)
\(=\left(x+1\right)\left(x^2+2x-3x-6\right)\)
\(=\left(x+1\right)\left[x\left(x+2\right)-3\left(x+2\right)\right]\)
\(=\left(x+1\right)\left(x+2\right)\left(x-3\right)\)
\(x^3-19x-30\)
\(=x^3-5x^2+5x^2-25x+6x-30\)
\(=x^2\left(x-5\right)+5x\left(x-5\right)+6\left(x-5\right)\)
\(=\left(x-5\right)\left(x^2+5x+6\right)\)
\(=\left(x-5\right)\left(x^2+2x+3x+6\right)\)
\(=\left(x-5\right)\left[x\left(x+2\right)+3\left(x+2\right)\right]\)
\(=\left(x-5\right)\left(x+3\right)\left(x+2\right)\)
Biểu thức này không phân tích được thành nhân tử nữa bạn nhé.
c ơi, lúc nãy e ghi nhầm đầu bài :(