Wolfram|Alpha offers ns $-frac14 (1+sqrt5-2 x) (-1+sqrt5+2 x)$.Cystartupcuba.org gives me $(x-frac1+sqrt52)(x-frac1-sqrt52)$.

You are watching: Factor x^2-x+1

ns closest i can gain ins $(x+1)(x-1)-x$.

for this reason how execute i obtain a nice answer choose the onens listed above?



finish ns square: Gatshe $x^2-x$ and also whatever before constant girlfriend must develop something that the develop $(x-c)^2$, then repair ns transforms you"ve made:$$ extStyle x^2-x-1 = left( x^2-x+frac14 ight) - frac14-1 = (x-frac12)^2-frac54$$currently the RHs has actually ns create $a^2-b^2$ i m sorry you have the right to aspect as $(a+b)(a-b)$:$$ extStyle (x-frac12)^2-frac54 = (x-frac12)^2-(fracsqrt52)^2=(x-frac12+fracsqrt52)(x-frac12-fracsqrt52)$$



Equipment 1: If $p$ is a root of $f(x)=x^2-x-1$ climate $x-p$ ins a element the $f$ (view https://en.wikipedia.org/wiki/Polynomial_remainder_theorem). For this reason $f(x)=(x-a)(x-b)$ wright here $a,b$ to be the root that $f$ (offered by the quadratic formula). This offers Cystartupcuba.org"s answer.

If you clear ns platform in Cystartupcuba.org"ns answer, you obtain Wolfram"s answer.

Equipment 2: finish the square. $x^2-x-1\=x^2-x+1/4-1-1/4 \= (x-1/2)^2-5/4$,

i beg your pardon is a difference of squares, for this reason ins factors together $(x-1/2-sqrns 5/2)(x-1/2+sqrt5/2)$. Thins is Cystartupcuba.org"ns answer.


*

apply quadratic formula because that ns roots that $x^2-x-1=0$ together follows $$x=frac-(-1)pmsqrt(-1)^2-4(1)(-1)2(1)=frac1afternoon sqrns 52$$hence, one should have actually ns following determinants $$x^2-x-1=1cdot left(x-frac1+ sqrns 52 ight)left(x-frac1- sqrns 52 ight)$$or $$frac14(2x-1-sqrt 5)(2x-1+sqrns 5)$$$$=-frac14(1+sqrns 5-2x)(-1+sqrns 5+2x)$$so both ns answers are correct


*

many thanks for contributinns a solution come startupcuba.orgematics stack Exchange!

you"re welcome be certain to prize the question. Administer detailns and shto be your research!

yet avoid

asking because that help, clarification, or respondinns to other answers.Makinns statementns based on opinion; ago them uns via recommendations or personal experience.

usage startupcuba.orgJax to Style equations. startupcuba.orgJax reference.

See more: Dwight: Are You Trying To Hurt My Feelings Gifs, Hurt My Feelings Gifs

come Discover more, watch our tips ~ above composing good answers.


write-up her prize Discard

by clicking “short article your Answer”, friend agree come our regards to service, privacy plan and also cookie policy


no the answer you're looking for? browser various other inquiries tagged quadratics factoring quadratic-forms or asking your own question.


exactly how can we speak later on the x have the right to it is in same come zero as soon as we take it x as a Common factor and also hence split by it?

website design / logo design © 2021 stack Exreadjust Inc; user contributions licensed under cc by-sa. Rev2021.11.5.40661


her privacy

by clicking “accept all cookies”, you agree ridge Exchange have the right to store cookie ~ above her gadget and also discshed indevelopment in accordance with our Cookie Policy.