All Exams Test series for 1 year @ ₹349 only
Question

What is the HCF of the polynomials x⁸ + x⁴ + 1 and x⁴ + x² + 1?

This question was previously asked in
CDS 2 2025 Maths Question Paper (14-Sep-2025)
The correct answer is

x⁴ + x² + 1

The highest common factor of the given polynomials is x⁴ + x² + 1. Therefore, the correct answer is (c) x⁴ + x² + 1.

Was this answer helpful?

Similar Questions

  1. Let \(p(x)\) be a polynomial. When \(p(x)\) is divided by \((x-1)\), it leaves 2 as the remainder. When \(p(x)\) is divided by \((x-2)\), it leaves 1 as the remainder. What is the remainder when \(p(x)\) is divided by \((x - 1)(x-2)\)?
  2. What is the remainder when \(x^6\) is divided by \(x^2 + 1\)?
  3. \((x+2)\) is a factor of which one of the following?
  4. If 2 is a zero of the polynomial \(p(x) = x^3 + 3x^2 - 6x - a\), then what is the sum of the squares of the other zeros of the polynomial?
  5. Suppose \(p(x) = x^4 + a_3x^3 + a_2x^2 + a_1x + a_0\) and \(q(x) = x^4 + b_3x^3 + b_2x^2 + b_1x + b_0\) are the polynomials. If \(\alpha, \beta, \gamma, \delta\) are zeros of \(p(x)\) and \(\alpha, \beta, \gamma, \lambda\) are zeros of \(q(x)\), then what is \(\frac{p(x) - q(x)}{(x - \alpha) (x - \beta) (x - \gamma)}\) equal to ?
  6. Consider the following in respect of the polynomial \(x^{4k} + x^{4k+2} + x^{4k+4} + x^{4k+6}\):
    1. The remainder is zero when the polynomial is divided by \(x^2 + 1\).
    2. The remainder is zero when the polynomial is divided by \(x^4 + 1\).
    Which of the statements given above is/are correct?
  7. If \(x^3 + px^2 + qx + r\) is an integer for all integral values of \(x\), then consider the following statements :
    I. \(p\) must be an integer
    II. \(q\) must be an integer
    III. \(r\) must be an integer
    Which of the statements given above is/are correct?
  8. Which of the following expressions can divide both the polynomials \(x^3+2x^2-5x+2\) and \(x^3+4x^2+x-6\) exactly ?
    I. \(x-1\)
    II. \(x+1\)
    III. \(x+2\)
    Select the correct answer using the code given below :
  9. If x² - 5x + 4 is a factor of x⁴ - px² + q, then what are the values of p and q respectively?


Important Questions from Polynomials

  1. If y 2= y + 7, then what is the value of y 3?

  2. Factorize x 2- y 2- 9z 2+ 6yz

  3. If one of the zeros of the polynomial x 3+ ax 2+ bx + c is  - 1, then the product of other two zeros is equal to :

  4. If a(a + b + c) 2 = 1792; b(a + b + c) 2 = 1536; c(a + b + c) 2 = 768, then what will be the value of b?

  5. If x = 3 so, what is the value of x 2 + 2x + 5 ?

Need Expert Advice?
Test Series
CDS img
Defence
UPSC CDS 2026 Mock Test Series
536 Tests 4 Tests Free
1671 Attempts
4.3(174)
English, Hindi
More Questions from CDS

Start Your Preparation with Prepp Mobile App

Download the app from Google Play & App Store
Download the app from Google Play & App Store
Prepp Mobile App