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Factor out
x⁵ + 2x⁴ + 4x³ + 8x² + 16x + 32
 one year ago
 one year ago
Let's have a little fun: Factor out x⁵ + 2x⁴ + 4x³ + 8x² + 16x + 32
 one year ago
 one year ago

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shubhamsrgBest ResponseYou've already chosen the best response.2
x^4 (x+2) + 4x^2(x+2) + 16(x+2)
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
\(S=x^5+2x^4+4x^3+8x^2+16x+32=32\cdot\left(\frac{x^5}{32}+\frac{x^4}{16}+\frac{x^3}{8}+\frac{x^2}{4}+\frac{x}{2}+1\right)\). \(S\cdot\frac x 2=32\cdot\left(\frac{x^6}{64}+\frac{x^5}{32}+\frac{x^4}{16}+\frac{x^3}{8}+\frac{x^2}{4}+\frac{x}{2}\right)\). Subtract the first equation from the second: \(S\cdot(\frac x 21)=32\cdot\left(\frac{x^6}{64}1\right)\). \(S=\frac{\left(\frac{x^3}{8}1\right)\left(\frac{x^3}{8}+1\right)}{(\frac x 21)}=\frac1{(\frac x21)}\cdot(\frac x 21)(\frac{x^2}4+\frac x 2+1)(\frac x 2+1)(\frac{x^2}4\frac x 2+1)=\) \(=(\frac{x^2}4+\frac x 2+1)(\frac x 2+1)(\frac{x^2}4\frac x 2+1)\).
 one year ago

klimenkovBest ResponseYou've already chosen the best response.1
Oh.. I forgot 32. \(S=(x^2+2 x+4)( x+2)(x^22 x+4)\).
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
\[x^5+2x^4+4x^3+8x^2+16x+32=\frac{x^632}{x2}\\=\frac{(x^38)(x^3+8)}{x2}=\frac{(x2)(x^2+2x+4)(x+2)(x^22x+4)}{x2}\\=(x+2)(x^2+2x+4)(x^22x+4)\]
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
oopd, that should be \[\frac{x^664}{x2}\]
 one year ago

zugzwangBest ResponseYou've already chosen the best response.0
Nice one, @sirm3d, the answer (and process) I was hoping for :)
 one year ago
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