Factoring a Septic Polynomial | How To Factor A Septic Polynomial | Aman Sir

In today's video, let's find the solution to a challenging question of Algebra.

We have to factorize a septic polynomial x^7+x^2+1

try to factor this septic polynomial, if you are able to factor the given polynomial then you have a very good knowledge of Algebra.

Let's see how we can solve this and understand How to factor a septic polynomial.

Factoring a septic polynomial. A challenge in algebra

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[mulayam.krkrkr]

एक बार पुनः दर्शन देने के लिए इस जादूगर को फिर से धन्यवाद ✌️✌️✌️

[avyakthaachar.]

Awesome method sir 👌
My method : Slight observation tells that omega (complex cube root of -1) and omega² are roots of the septic. So (x-omega)(x-omega²) = x²+x+1 is a factor of the septic. The other factor can be found by polynomial long division.

[arpit]

love from nepal sir you made my maths very welll🥰🥰

[Zuhaib]

Sir apki videos se mere maths k concepts aur approach of question bohot achi Hui h. Thanks for your content. You are really a brilliant teacher OF MATHEMATICS!!

[Shubham-f]

A big thanks for aman sir for giving such interesting problems to us

[dhairyasakhare]

Really I used to in a way hate the subject but you woke up the curiosity of the subject in me
Thankyou sir

[adityaaggarwal]

Literally amazing enjoying these videos sir ❤️❤️❤️❤️❤️

[StudBud]

It's an amazing video sir!
Couldn't solve the problem by myself but the process was fun 😃

[samirakishan]

Luv u sir for ur elaboration... Sameer from ODISHA

[nityajungade]

Sir I think you will become the next VK Bansal

[Physicslover]

हामी त mathematics 💕 lover 😍 हो ।।। सर ✍️🍀

[uttammodi]

Sir, we can do it by hit and trial method since coefficient is 1 but ±1 is not the root of the septic polynomial, thus there might exist imaginary roots, so if we check ±i, equation is again not satisfying. Now check it as w, w² the equation is satisfying


So, (x-w)(x-w²) = (x²+x+1) is a factor of this polynomial, now devide it by (x²+x+1), we get another factor (x⁵-x⁴+x²-x+1).

[bikramshahi]

I want to reward as the best mathematics teacher.

[shashikalapatel]

Sir Indian Statistical Institute ke jo portion jee se alag hai wo app please alag se padha dijiye please sir 🙏🙏🙏🙏🙏

[akshaj_]

Sir can you please tell how to build such an approach for solving more problems

[seemarani]

Sir this cane also be solved by
w and w^2 are the roots of this equation from them we find a quadratic equation then simply divide them

[sanjaylal]

I tried w to be a root and therefore w² is also a root as the septic polynomial have real coefficient then factorised it to (x^2+x+1)(x^5-x^4...)
And further tried fouth root of unity to satisfy.even it isnt factorised further.

[emondhara]

Sir i am in class 8 but still I really love maths

[honestadministrator]

If any polynomial is reduced to
k ( x^2 + x + 1) at x^3 = 1
Then x^2 +.x + 1 is a factor of aforesaid polynomial.

Herein x^7 + x^2 + 1
= (x^2 + x + 1)(x^5 - x^4 +x^2 - x + 1)

[Qayammehdiimtiaz]

My favourite teacher
Love you a lot sir
😊😊😊