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x^4-4x-1
= x^4 + 4 + 4x² - 4x² = ( x² + 2 )² - 4x² = ( x² + 2 - 2x )( x² + 2 + 2x )
hoặc
x^4-4x-1
=(x^2)^2+4x^2+4-4x^2
=(x^2+2)^2-4x^2
=(x^2-2x+2)(x^2+2x+2)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(-2x^3+x^2+12\)
\(=-2x^3+4x^2-3x^2+6x-6x+12\)
\(=-2x^2\left(x-2\right)-3x\left(x-2\right)-6\left(x-2\right)\)
\(=\left(x-2\right)\left(-2x^2-3x-6\right)\)
\(8x^4+81\)
\(=8x^4+2\cdot2\sqrt{2}\cdot x^2\cdot9+81-36\sqrt{2}\cdot x^2\)
\(=\left(2\sqrt{2}x^2+9\right)^2-\left(6\sqrt[4]{2}\cdot x\right)^2\)
\(=\left(2\sqrt{2}\cdot x^2-6\sqrt[4]{2}\cdot x+9\right)\left(2\sqrt{2}\cdot x^2+6\sqrt[4]{2}\cdot x+9\right)\)
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\(a,\left(x^2+4x+8\right)^2+3x\left(x^2+4x+8\right)+2x^2\) (sửa \(2x\rightarrow2x^2\)
Đặt \(x^2+4x+8=a\)
\(=a^2+3ax+2x=a^2+ax+2ax+2x^2=\left(a+x\right)\left(a+2x\right)\\ =\left(x^2+5x+8\right)\left(x^2+6x+8\right)=\left(x^2+5x+8\right)\left(x+2\right)\left(x+4\right)\)
\(\left(x^2+4x+8\right)^2+3x\left(x^2+4x+8\right)+2x\)
\(=\left(x^2+6x+8\right)\left(x^2+5x+8\right)\)
\(=\left(x+2\right)\left(x+4\right)\left(x^2+5x+8\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1:
$5x+10=5(x+2)$
Bài 2:
Tại $x=8$ thì $x^2+4x+4=(x+2)^2=(8+2)^2=10^2=100$
Bài 3:
$x^2-6x+9=x^2-2.3.x+3^2=(x-3)^2$
Bài 4:
Diện tích mảnh đất là:
$(x+5)(x-5)=24$
$\Leftrightarrow x^2-25=24$
$\Leftrightarrow x^2=49$
$\Rightarrow x=7$ (do $x>5$)
Chiều dài mảnh đất là: $x+5=7+5=12$ (m)
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2x2+3x-5
<=> 2x2+5x-2x-5
<=>(2x2+5x)-(2x+5)
<=>x(2x+5)-1(2x+5)
<=> (x-1)(2x+5)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^4-6x^3+54x-81\)
\(=x^4+3x^3-9x^3+27x^2-27x^2 +81x-27x-81\)
\(=\left(x^4+3x^3\right)-\left(9x^3+27x^2\right)+\left(27x^2+81x\right)-\left(27+81\right)\)
\(=x^3\left(x+3\right)-9x^2\left(x+3\right)+27x\left(x+3\right)-27\left(x+3\right)\)
\(=\left(x+3\right)\left(x^3-9x^2+27x-27\right)\)
\(=\left(x+3\right)\left(x-3\right)^3\)
\(81.x^2+4\)
\(=81.\left(x^2+2^2\right)\)
\(=81.\left(x+2\right)\left(x-2\right)\)
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