One of the factors of x^88+x^69+x^50+x^43 is (a) x+1 (b) x+i (c) x-i (d) All the above

Name: Problem 156, Chapter 1: IIT JEE Super Course in Mathematics ALGEBRA II
Uploaded: 2021-07-22T11:28:51-08:00
Duration: 6 min 24 s
Channel: Uma Kumari
Description: One of the factors of x^88+x^69+x^50+x^43 is (a) x+1 (b) x+i (c) x-i (d) All the above

step 1 In this question we need to find the factors of x to the power 88 plus x to the power 69 plus x

One of the factors of x^88+x^69+x^50+x^43 is (a) x+1 (b) x+i...

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Key Concepts

Polynomial Factorization

This concept involves expressing a polynomial as a product of lower-degree polynomials. It is a fundamental technique in algebra that simplifies the analysis of polynomial equations and helps reveal their roots and other properties.

Factor Theorem

The factor theorem states that a polynomial f(x) has a factor (x - a) if and only if f(a) = 0. This principle is widely used to test potential factors by evaluating the polynomial at specific values, thereby confirming the factorization.

Complex Numbers in Polynomial Equations

Complex numbers extend the field of real numbers and allow polynomials to have roots even when no real solutions exist. They are essential in understanding and factoring polynomials, as every non-constant polynomial has a complete set of roots in the complex number system, according to the Fundamental Theorem of Algebra.

Properties of Exponents

Understanding the rules of exponents is crucial when dealing with high-degree polynomials. These properties allow for the simplification and manipulation of expressions, making techniques like substitution or factoring by grouping more effective.

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