Maths practice › Class 10 › Division AlgorithmClass 10 Division Algorithm — practice questions with answers
Algebra — Polynomials · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. In the Division Algorithm for polynomials, p(x) = g(x) x q(x) + r(x). What does p(x) represent?
A Dividend B Divisor C Quotient D Remainder Show answer Answer: A) Dividend
p(x) is the polynomial being divided, so it is the dividend. g(x) is divisor, q(x) is quotient, r(x) is remainder.
2. In p(x) = g(x) x q(x) + r(x), if deg p(x) = 4 and deg q(x) = 1, what is deg g(x)?
Show answer Answer: A) 3
deg g(x) = deg p(x) - deg q(x) = 4 - 1 = 3 (when remainder degree is smaller).
3. The degree of the remainder when dividing by x³ + 2x is at most:
Show answer Answer: A) 2
The divisor has degree 3, so the remainder has degree less than 3, i.e. at most 2.
4. On dividing x⁴ + 1 by x² + 1, what is the remainder?
Show answer Answer: C) 2
x⁴ + 1 = (x² + 1)(x² - 1) + 2. Quotient = x² - 1, remainder = 2.
5. A polynomial p(x) leaves remainder 2 when divided by (x - 1) and remainder 4 when divided by (x - 3).
Show answer Answer: A) 1
From a + b = 2 and a = 1, we get b = 1. (Check: 3a + b = 3 + 1 = 4, correct.)