Class 10 > Mathematics (Maths) Class 10 > Exercise 2.3 NCERT Solutions - Polynomials (Old Syllabus)
Exercise 2.3 NCERT Solutions - Polynomials (Old Syllabus) - Mathematics (Maths) Class 10
Q.1. Find the remainder when x3+3x2+3x+1 is divided by
(i) x+1
Solution:
x+1= 0
⇒ x = −1
∴ Remainder:
p(−1) = (−1)3+3(−1)2+3(−1)+1
= −1+3−3+1
= 0
(ii) x−1/2
Solution:
x-1/2 = 0
⇒ x = 1/2
∴ Remainder:
p(1/2) = (1/2)3+3(1/2)2+3(1/2)+1
= (1/8)+(3/4)+(3/2)+1
= 27/8
(iii) x
Solution:
x = 0
∴ Remainder:
p(0) = (0)3+3(0)2+3(0)+1
= 1
(iv) x+π
Solution:
x+π = 0
⇒ x = −π
∴ Remainder:
p(0) = (−π)3 +3(−π)2+3(−π)+1
= −π3+3π2−3π+1
(v) 5+2x
Solution:
5+2x=0
⇒ 2x = −5
⇒ x = -5/2
∴ Remainder:
(-5/2)3+3(-5/2)2+3(-5/2)+1 = (-125/8)+(75/4)-(15/2)+1
= -27/8
Q.2. Find the remainder when x3−ax2+6x−a is divided by x-a.
Solution:
Let p(x) = x3−ax2+6x−a
x−a = 0
∴ x = a
Remainder:
p(a) = (a)3−a(a2)+6(a)−a = a3−a3+6a−a = 5a
Q.3. Check whether 7+3x is a factor of 3x3+7x.
Solution:
7+3x = 0
⇒ 3x = −7
⇒ x = -7/3
∴ Remainder:
3(-7/3)3+7(-7/3) = -(343/9)+(-49/3)
= (-343-(49)3)/9
= (-343-147)/9
= -490/9 ≠ 0
∴ 7+3x is not a factor of 3x3+7x
Check out the NCERT Solutions of all the exercises of Polynomials:
Exercise 2.1. NCERT Solutions: Polynomials
The document Exercise 2.3 NCERT Solutions - Polynomials (Old Syllabus) | Mathematics (Maths) Class 10 is a part of the Class 10 Course Mathematics (Maths) Class 10.
All you need of Class 10 at this link: Class 10
FAQs on Exercise 2.3 NCERT Solutions - Polynomials (Old Syllabus) - Mathematics (Maths) Class 10
| 1. What is a polynomial? |  |
Ans. A polynomial is an algebraic expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication operations. It can have one or more terms, and the degree of a polynomial is determined by the highest power of the variable in the expression.
| 2. How do you classify polynomials based on the number of terms? | |
Ans. Polynomials can be classified based on the number of terms they have. A polynomial with one term is called a monomial, with two terms is called a binomial, and with three terms is called a trinomial. Polynomials with more than three terms are generally referred to as polynomials.
| 3. What is the degree of a polynomial? | |
Ans. The degree of a polynomial is determined by the highest power of the variable in the expression. For example, if a polynomial has the term 3x^2, then the degree of the polynomial is 2. The degree helps in understanding the behavior of the polynomial and its graph.
| 4. How do you add or subtract polynomials? | |
Ans. To add or subtract polynomials, you need to combine like terms. Like terms are terms that have the same variable(s) raised to the same power. Simply add or subtract the coefficients of the like terms while keeping the variables and exponents unchanged. If there are no like terms, the polynomials cannot be added or subtracted.
| 5. How do you find the zeroes of a polynomial? | |
Ans. To find the zeroes of a polynomial, you need to solve the polynomial equation where the polynomial is set equal to zero. The zeroes of a polynomial are the values of the variable for which the polynomial evaluates to zero. You can use various methods such as factorization, synthetic division, or using the quadratic formula depending on the degree of the polynomial.
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