Please enter the following details
Free Daily Targets & Mocks
Study Material & Formulas PDFs
1 on 1 Mentorship
Question 79
Consider a function $$f(x) = x^4 + x^3 + x^2 + x + 1$$, where x is a positive integer greater than 1. What will be the remainder if $$f(x^5)$$ is divided by f(x)?
Solution
$$x^5-1 = (x-1)(x^4+x^3+x^2+x+1)$$
$$x^5-1=(x-1)f(x)$$
$$x^5 = 1+(x-1)f(x)$$
$$f(x^5) = (1+(x-1)f(x))^4+(1+(x-1)f(x))^3+(1+(x-1)f(x))^2+(1+(x-1)f(x))+1$$
On dividing by $$f(x)$$, every term will leave $$1$$ as the remainder. Therefore, the remainder when $$f(x^5)$$ is divided by $$f(x)$$ is $$1+1+1+1+1=5$$.
Therefore, option A is the right answer.
Create a FREE account and get:
- All Quant Formulas and shortcuts PDF
- 15 XAT previous papers with solutions PDF
- XAT Trial Classes for FREE
XAT Quant Questions | XAT Quantitative Ability
XAT Venn Diagrams QuestionsXAT Data Sufficiency QuestionsXAT Time, Distance and Work QuestionsXAT Progressions and Series QuestionsXAT Averages, Ratio and Proportion Questions
XAT DILR Questions | LRDI Questions For XAT
XAT Games and Tournamnents QuestionsXAT Puzzles QuestionsXAT Logical Reasoning QuestionsXAT Data Interpretation QuestionsXAT Scheduling Questions
