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a, \(x^5+x^4+1\)
\(\Leftrightarrow x^5+x^4-x^2+\frac{1}{4}-\frac{1}{4}+x^2\)
\(\Leftrightarrow x^5+\left(x^2-\frac{1}{2}\right)^2-\frac{1}{4}+x^2\)
\(\Leftrightarrow x^2\left(x^3+1\right)+\left(x^2-\frac{1}{2}\right)^2-\frac{1}{4}\)
\(\Leftrightarrow x^2\left(x+1\right)\left(x^2-x+1\right)+\left(x^2-\frac{1}{2}+\frac{1}{2}\right)\left(x^2-\frac{1}{2}-\frac{1}{2}\right)\)
ta có :x^5 +x^4 +1=x^5-x^2 +x^4 -x +x^2 +x +1=x^2(x^3-1) +x(x^3 -1)+x^2 +x +1=x^2(x-1)(x^2+x+1)+x(x-1)(x^2 +x+1) +x^2 +x +1=(x^2 +x +1)(x^3 -x^2 +x^2 -x +1)=(x^2 +x+1)(x^3-x+1)
\(x^4+4\)
\(=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-4x^2\)
\(=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)
a) \(x^4+324=\left(x^2-6x+18\right)\left(x^2+6x+18\right)\)
c) \(x^{13}+x^5+1=\left(x^2+x+1\right)\left(x^{11}-x^{10}+x^8-x^7+x^5-x^4+x^3-x+1\right)\)
d) \(x^{11}+x+1=\left(x^2+x+1\right)\left(x^9-x^8+x^6-x^5+x^3-x^2+1\right)\)
e) \(x^8+3x^4+4=\left(x^4+x^2+2\right)\left(x^4-x^2+2\right)\)
x7+x6+x5-x6-x5-x4+x5+x4+x3-x3-x2-x1+x2+x1+1
= x5(x2+x+1) - x4(x2+x+1)+x3(x2+x+1)-x(x2+x+1) +(x2+x+1)
=(x2+x+1)( x5-x4+x3-x+1)
────(♥)(♥)(♥)────(♥)(♥)(♥) __ ɪƒ ƴσυ’ʀє αʟσηє,
──(♥)██████(♥)(♥)██████(♥) ɪ’ʟʟ ɓє ƴσυʀ ѕɧα∂σѡ.
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──(♥)████████████████(♥) ɪƒ ƴσυ ѡαηт α ɧυɢ,
────(♥)████████████(♥) __ ɪ’ʟʟ ɓє ƴσυʀ ρɪʟʟσѡ.
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───────────(♥) __ ɪ’ʟʟ ʝυѕт ɓє ɱє.
Ta có : x5 + x + 1
= x5 + x4 + x3 + x2 + x + 1 - x4 - x3 - x2
= (x5 + x4 + x3) + (x2 + x + 1) - (x4 + x3 + x2)
= x3(x2 + x + 1) + (x2 + x + 1) - x2(x2 + x + 1)
= (x2 + x + 1)(x3 - x2 + 1) .
Ta có : x5 + x + 1
= x5 + x4 + x3 + x2 + x + 1 - x4 - x3 - x2
= (x5 + x4 + x3) + (x2 + x + 1) - (x4 + x3 + x2)
= x3(x2 + x + 1) + (x2 + x + 1) - x2(x2 + x + 1)
= (x2 + x + 1)(x3 - x2 + 1) .
x8 + x4 + 1
= x8 + 2x4 + 1 - x4
= [(x4)2 + 2x4 + 1] - x4
= (x4 + 1)2 - (x2)2
= ( x4 - x2 + 1 ) ( x4 + x2 + 1 )
x8+x+1
=(x8−x2)+(x2+x+1)
=x2(x6−1)+(x2+x+1)
=x2(x2+1)(x3−1)+(x2+x+1)
=x2(x3+1)(x−1)(x2+x+1)+(x2+x+1)
=(x2+x+1)[x2(x3+1)(x−1)+1]
=(x2+x+1)[x2(x4−x3+x−1)+1]
=(x2+x+1)(x6−x5+x3−x2+1)
x^4+x^2+1 = (x^4+2x^2+1)-x^2 = (x^2+1)^2-x^2 = (x^2-x+1).(x^2+x+1)
k mk nha
x5-x4-1=x5-x3-x2-x4+x2+x+x3-x-1
=x2.(x3-x-1)-x.(x3-x-1)+(x3-x-1)
=(x3-x-1)(x2-x+1)
x^4+x^2+1 = (x^4+2x^2+1)-x^2 = (x^2+1)^2-x^2 = (x^2-x+1).(x^2+x+1)
k mk nha