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mk ghi đáp án, còn lại bạn tự biến đổi
a) \(2x^3-x^2+5x+3=\left(2x+1\right)\left(x^2-x+3\right)\)
b) \(x^3+5x^2+8x+4=\left(x+1\right)\left(x+2\right)^2\)
c) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)
d) \(4x^4+1=\left(2x^2-2x+1\right)\left(2x^2+2x+1\right)\)
e) \(x^4-7x^3+14x^2-7x+1=\left(x^2-4x+1\right)\left(x^2-3x+1\right)\)
mk làm chi tiết theo yêu của của người hỏi đề:
a) \(2x^3-x^2+5x+3\)
\(=\left(2x^3-2x^2+6x\right)+\left(x^2-x+3\right)\)
\(=2x\left(x^2-x+3\right)+\left(x^2-x+3\right)\)
\(=\left(2x+1\right)\left(x^2-x+3\right)\)
b) \(x^3+5x^2+8x+4\)
\(=\left(x^3+4x^2+4x\right)+\left(x^2+4x+4\right)\)
\(=x\left(x^2+4x+4\right)+\left(x^2+4x+4\right)\)
\(=\left(x+1\right)\left(x^2+4x+4\right)\)
\(=\left(x+1\right)\left(x+2\right)^2\)
\(x^8+x^4+1\)
\(=\left(x^8+2x^4+1\right)-x^4\)
\(=\left(x^4+1\right)^2-x^4\)
\(=\left(x^4+1-x^2\right)\left(x^4+1+x^2\right)\)
\(=\left(x^4-x^2+1\right)\left(x^4+2x^2-x^2+1\right)\)
\(=\left(x^4-x^2+1\right)[\left(x^2+1\right)^2-x^2]\)
\(=\left(x^4-x^2+1\right)\left(x^2+1-x\right)\left(x^2+1+x\right)\)
Bài 2:
a)A= \(6x^2\)\(-11x+3\)
<=>A=\(6x^2\)\(-2x-9x+3\)
<=>A=(\(6x^2\)\(-2x\))-\(\left(9x-3\right)\)
=>A=\(2x\left(3x-1\right)\)\(-3\left(3x+1\right)\)
<=>A=\(2x\left(3x-1\right)+3\left(3x-1\right)\)
=>A=(3x-1)(2x+3)
Biết làm mỗi 2 câu thôi -.-
a) \(15xy-20x^2=5x\left(3y-4x\right)\)
d) \(2x^2-7x+5=2x^2-2x-5x+5\)
\(=2x\left(x-1\right)-5\left(x-1\right)=\left(2x-5\right)\left(x-1\right)\)
a) \(15xy-20x^2\)
\(=5x\left(3y-4x\right)\)
b) \(\left(x-4\right)^2-\left(y-5\right)^2\)
\(=\left[x-4-\left(y-5\right)\right]\cdot\left(x-4+y-5\right)\)
\(=\left(x-4-y+5\right)\left(x-9+y\right)\)
\(=\left(x+1-y\right)\left(x-9+y\right)\)
c) \(x^4-9x^3-x^2+9x\)
\(=x\left(x^3-9x^2-x+9\right)\)
\(=x\cdot\left[x^2\cdot\left(x-9\right)-\left(x-9\right)\right]\)
\(=x\left(x^2-1\right)\left(x-9\right)\)
\(=x\left(x-1\right)\left(x+1\right)\left(x-9\right)\)
d) \(2x^2-7x+5\)
\(=2x^2-2x-5x+5\)
\(=2x\left(x-1\right)-5\left(x-1\right)\)
\(=\left(2x-5\right)\left(x-1\right)\)