Rešite (x-1)(x-2)(x-3)(x-4)(114505/24)+2x-1

$$(x-1)(x-2)(x-3)(x-4)( \frac{ 114505 }{ 24 } )+2x-1$$

Ovrednoti

$$\frac{114505x^{4}}{24}-\frac{572525x^{3}}{12}+\frac{4007675x^{2}}{24}-\frac{2862601x}{12}+114504$$

Koraki rešitve

Uporabite distributivnost tako, da pomnožite vsako vrednost x-1 z vsako vrednostjo x-2.

$$\left(x^{2}-2x-x+2\right)\left(x-3\right)\left(x-4\right)\times \frac{114505}{24}+2x-1$$

Združite -2x in -x, da dobite -3x.

$$\left(x^{2}-3x+2\right)\left(x-3\right)\left(x-4\right)\times \frac{114505}{24}+2x-1$$

Uporabite distributivnost tako, da pomnožite vsako vrednost x^{2}-3x+2 z vsako vrednostjo x-3.

$$\left(x^{3}-3x^{2}-3x^{2}+9x+2x-6\right)\left(x-4\right)\times \frac{114505}{24}+2x-1$$

Združite -3x^{2} in -3x^{2}, da dobite -6x^{2}.

$$\left(x^{3}-6x^{2}+9x+2x-6\right)\left(x-4\right)\times \frac{114505}{24}+2x-1$$

Združite 9x in 2x, da dobite 11x.

$$\left(x^{3}-6x^{2}+11x-6\right)\left(x-4\right)\times \frac{114505}{24}+2x-1$$

Uporabite distributivnost tako, da pomnožite vsako vrednost x^{3}-6x^{2}+11x-6 z vsako vrednostjo x-4.

$$\left(x^{4}-4x^{3}-6x^{3}+24x^{2}+11x^{2}-44x-6x+24\right)\times \frac{114505}{24}+2x-1$$

Združite -4x^{3} in -6x^{3}, da dobite -10x^{3}.

$$\left(x^{4}-10x^{3}+24x^{2}+11x^{2}-44x-6x+24\right)\times \frac{114505}{24}+2x-1$$

Združite 24x^{2} in 11x^{2}, da dobite 35x^{2}.

$$\left(x^{4}-10x^{3}+35x^{2}-44x-6x+24\right)\times \frac{114505}{24}+2x-1$$

Združite -44x in -6x, da dobite -50x.

$$\left(x^{4}-10x^{3}+35x^{2}-50x+24\right)\times \frac{114505}{24}+2x-1$$

Uporabite distributivnost, da pomnožite x^{4}-10x^{3}+35x^{2}-50x+24 s/z \frac{114505}{24}.

$$x^{4}\times \frac{114505}{24}-10x^{3}\times \frac{114505}{24}+35x^{2}\times \frac{114505}{24}-50x\times \frac{114505}{24}+24\times \frac{114505}{24}+2x-1$$

Izrazite -10\times \frac{114505}{24} kot enojni ulomek.

$$x^{4}\times \frac{114505}{24}+\frac{-10\times 114505}{24}x^{3}+35x^{2}\times \frac{114505}{24}-50x\times \frac{114505}{24}+24\times \frac{114505}{24}+2x-1$$

Pomnožite -10 in 114505, da dobite -1145050.

$$x^{4}\times \frac{114505}{24}+\frac{-1145050}{24}x^{3}+35x^{2}\times \frac{114505}{24}-50x\times \frac{114505}{24}+24\times \frac{114505}{24}+2x-1$$

Zmanjšajte ulomek \frac{-1145050}{24} na najmanjši imenovalec tako, da izpeljete in okrajšate 2.

$$x^{4}\times \frac{114505}{24}-\frac{572525}{12}x^{3}+35x^{2}\times \frac{114505}{24}-50x\times \frac{114505}{24}+24\times \frac{114505}{24}+2x-1$$

Izrazite 35\times \frac{114505}{24} kot enojni ulomek.

$$x^{4}\times \frac{114505}{24}-\frac{572525}{12}x^{3}+\frac{35\times 114505}{24}x^{2}-50x\times \frac{114505}{24}+24\times \frac{114505}{24}+2x-1$$

Pomnožite 35 in 114505, da dobite 4007675.

$$x^{4}\times \frac{114505}{24}-\frac{572525}{12}x^{3}+\frac{4007675}{24}x^{2}-50x\times \frac{114505}{24}+24\times \frac{114505}{24}+2x-1$$

Izrazite -50\times \frac{114505}{24} kot enojni ulomek.

$$x^{4}\times \frac{114505}{24}-\frac{572525}{12}x^{3}+\frac{4007675}{24}x^{2}+\frac{-50\times 114505}{24}x+24\times \frac{114505}{24}+2x-1$$

Pomnožite -50 in 114505, da dobite -5725250.

$$x^{4}\times \frac{114505}{24}-\frac{572525}{12}x^{3}+\frac{4007675}{24}x^{2}+\frac{-5725250}{24}x+24\times \frac{114505}{24}+2x-1$$

Zmanjšajte ulomek \frac{-5725250}{24} na najmanjši imenovalec tako, da izpeljete in okrajšate 2.

$$x^{4}\times \frac{114505}{24}-\frac{572525}{12}x^{3}+\frac{4007675}{24}x^{2}-\frac{2862625}{12}x+24\times \frac{114505}{24}+2x-1$$

Okrajšaj 24 in 24.

$$x^{4}\times \frac{114505}{24}-\frac{572525}{12}x^{3}+\frac{4007675}{24}x^{2}-\frac{2862625}{12}x+114505+2x-1$$

Združite -\frac{2862625}{12}x in 2x, da dobite -\frac{2862601}{12}x.

$$x^{4}\times \frac{114505}{24}-\frac{572525}{12}x^{3}+\frac{4007675}{24}x^{2}-\frac{2862601}{12}x+114505-1$$

Odštejte 1 od 114505, da dobite 114504.

$$x^{4}\times \frac{114505}{24}-\frac{572525}{12}x^{3}+\frac{4007675}{24}x^{2}-\frac{2862601}{12}x+114504$$

Razširi

$$\frac{114505x^{4}}{24}-\frac{572525x^{3}}{12}+\frac{4007675x^{2}}{24}-\frac{2862601x}{12}+114504$$

Koraki rešitve

Uporabite distributivnost tako, da pomnožite vsako vrednost x-1 z vsako vrednostjo x-2.

$$\left(x^{2}-2x-x+2\right)\left(x-3\right)\left(x-4\right)\times \frac{114505}{24}+2x-1$$

Združite -2x in -x, da dobite -3x.

$$\left(x^{2}-3x+2\right)\left(x-3\right)\left(x-4\right)\times \frac{114505}{24}+2x-1$$

Uporabite distributivnost tako, da pomnožite vsako vrednost x^{2}-3x+2 z vsako vrednostjo x-3.

$$\left(x^{3}-3x^{2}-3x^{2}+9x+2x-6\right)\left(x-4\right)\times \frac{114505}{24}+2x-1$$

Združite -3x^{2} in -3x^{2}, da dobite -6x^{2}.

$$\left(x^{3}-6x^{2}+9x+2x-6\right)\left(x-4\right)\times \frac{114505}{24}+2x-1$$

Združite 9x in 2x, da dobite 11x.

$$\left(x^{3}-6x^{2}+11x-6\right)\left(x-4\right)\times \frac{114505}{24}+2x-1$$

Uporabite distributivnost tako, da pomnožite vsako vrednost x^{3}-6x^{2}+11x-6 z vsako vrednostjo x-4.

$$\left(x^{4}-4x^{3}-6x^{3}+24x^{2}+11x^{2}-44x-6x+24\right)\times \frac{114505}{24}+2x-1$$

Združite -4x^{3} in -6x^{3}, da dobite -10x^{3}.

$$\left(x^{4}-10x^{3}+24x^{2}+11x^{2}-44x-6x+24\right)\times \frac{114505}{24}+2x-1$$

Združite 24x^{2} in 11x^{2}, da dobite 35x^{2}.

$$\left(x^{4}-10x^{3}+35x^{2}-44x-6x+24\right)\times \frac{114505}{24}+2x-1$$

Združite -44x in -6x, da dobite -50x.

$$\left(x^{4}-10x^{3}+35x^{2}-50x+24\right)\times \frac{114505}{24}+2x-1$$

Uporabite distributivnost, da pomnožite x^{4}-10x^{3}+35x^{2}-50x+24 s/z \frac{114505}{24}.

$$x^{4}\times \frac{114505}{24}-10x^{3}\times \frac{114505}{24}+35x^{2}\times \frac{114505}{24}-50x\times \frac{114505}{24}+24\times \frac{114505}{24}+2x-1$$

Izrazite -10\times \frac{114505}{24} kot enojni ulomek.

$$x^{4}\times \frac{114505}{24}+\frac{-10\times 114505}{24}x^{3}+35x^{2}\times \frac{114505}{24}-50x\times \frac{114505}{24}+24\times \frac{114505}{24}+2x-1$$

Pomnožite -10 in 114505, da dobite -1145050.

$$x^{4}\times \frac{114505}{24}+\frac{-1145050}{24}x^{3}+35x^{2}\times \frac{114505}{24}-50x\times \frac{114505}{24}+24\times \frac{114505}{24}+2x-1$$

Zmanjšajte ulomek \frac{-1145050}{24} na najmanjši imenovalec tako, da izpeljete in okrajšate 2.

$$x^{4}\times \frac{114505}{24}-\frac{572525}{12}x^{3}+35x^{2}\times \frac{114505}{24}-50x\times \frac{114505}{24}+24\times \frac{114505}{24}+2x-1$$

Izrazite 35\times \frac{114505}{24} kot enojni ulomek.

$$x^{4}\times \frac{114505}{24}-\frac{572525}{12}x^{3}+\frac{35\times 114505}{24}x^{2}-50x\times \frac{114505}{24}+24\times \frac{114505}{24}+2x-1$$

Pomnožite 35 in 114505, da dobite 4007675.

$$x^{4}\times \frac{114505}{24}-\frac{572525}{12}x^{3}+\frac{4007675}{24}x^{2}-50x\times \frac{114505}{24}+24\times \frac{114505}{24}+2x-1$$

Izrazite -50\times \frac{114505}{24} kot enojni ulomek.

$$x^{4}\times \frac{114505}{24}-\frac{572525}{12}x^{3}+\frac{4007675}{24}x^{2}+\frac{-50\times 114505}{24}x+24\times \frac{114505}{24}+2x-1$$

Pomnožite -50 in 114505, da dobite -5725250.

$$x^{4}\times \frac{114505}{24}-\frac{572525}{12}x^{3}+\frac{4007675}{24}x^{2}+\frac{-5725250}{24}x+24\times \frac{114505}{24}+2x-1$$

Zmanjšajte ulomek \frac{-5725250}{24} na najmanjši imenovalec tako, da izpeljete in okrajšate 2.

$$x^{4}\times \frac{114505}{24}-\frac{572525}{12}x^{3}+\frac{4007675}{24}x^{2}-\frac{2862625}{12}x+24\times \frac{114505}{24}+2x-1$$

Okrajšaj 24 in 24.

$$x^{4}\times \frac{114505}{24}-\frac{572525}{12}x^{3}+\frac{4007675}{24}x^{2}-\frac{2862625}{12}x+114505+2x-1$$

Združite -\frac{2862625}{12}x in 2x, da dobite -\frac{2862601}{12}x.

$$x^{4}\times \frac{114505}{24}-\frac{572525}{12}x^{3}+\frac{4007675}{24}x^{2}-\frac{2862601}{12}x+114505-1$$

Odštejte 1 od 114505, da dobite 114504.

$$x^{4}\times \frac{114505}{24}-\frac{572525}{12}x^{3}+\frac{4007675}{24}x^{2}-\frac{2862601}{12}x+114504$$