Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.
(i) t2 – 3, 2t4 + 3t3 – 2t2– 9t – 12
(ii) x2 + 3x + 1, 3x4 + 5x3 – 7x2 + 2x + 2
(iii) x2 + 3x + 1, x5 – 4x3 + x2 + 3x + 1
Ex 2.3 Class 10 Maths Question 3.
Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are and \(\sqrt { \frac { 5 }{ 3 } }\) and –\(\sqrt { \frac { 5 }{ 3 } }\)
Solution:
Ex 2.3 Class 10 Maths Question 4.
On dividing x3 – 3x2 + x + 2bya polynomial g(x), the quotient and remainder were x – 2 and -2x + 4 respectively. Find g(x).
Solution:
Ex 2.3 Class 10 Maths Question 5.
Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and:
(i) deg p(x) = deg q(x)
(ii) deg q(x) = deg r(x)
(iii) deg r(x) = 0
Solution:
CBSE Class 10 Polynomials — Complete Guide
Polynomials is a scoring chapter in CBSE Class 10 Mathematics, worth 3-4 marks. Master the zeros-coefficient relationship and division algorithm for guaranteed marks.
Quick Revision: Key Concepts
- Zeros: Values of x where p(x) = 0 (x-intercepts on graph)
- Sum of zeros (α + β): −b/a
- Product of zeros (αβ): c/a
- Form polynomial: k[x² − (sum)x + (product)]
- Division algorithm: p(x) = g(x) × q(x) + r(x)
Board Exam Pattern
1-2 MCQs on zeros-coefficient relationship, 1 short answer on finding zeros and verifying relationship or forming a polynomial from given zeros.
Most Important Questions
- Find zeros of a quadratic polynomial and verify sum/product relationship
- Find quadratic polynomial with given sum and product of zeros
- Divide one polynomial by another and verify division algorithm
- Find remaining zeros given one or two zeros
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