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Class 9 Maths NCERT Solution for Polynomial part 1




In this page we have NCERT book Solutions for Class 9th Maths:Polynomial for EXERCISE 1 . Hope you like them and do not forget to like , social share and comment at the end of the page.
Question 1:
Which of the following expressions are polynomials in one variable and which are
not? State reasons for your answer.
4x2– 3x + 7
y2 + √2
3 √t + t√ 2
 y + 2/y
x10 + y3 + t50
Solution:
(i) 4x2– 3x + 7
Yes, this expression is a polynomial in one variable x.
(ii) y2 + √2
Yes, this expression is a polynomial in one variable y.
(iii) 3 √t + t√ 2
 No. It can be observed that the exponent of variable t in term 3 √t is 1/2, which is not a whole number. Therefore, this expression is not a polynomial.
(iv) y+2/y  No. It can be observed that the exponent of variable y in term 2/y is -1 which is not a whole number. Therefore, this expression is not a polynomial.
(v) x10 + y3 + t50
No. It can be observed that this expression is a polynomial in 3 variables x, y, and t. Therefore, it is not a polynomial in one variable.
Question 2.
Write the coefficients of x2 in each of the following:
  1. 2 + x2 + x
  2. 2 – x2 + x3
  3. (π/2)x2 + x
  4. √ 2  x −1
Solution:
(i) 2+x2+x
 Coefficient of x2 is 1.
 (ii)  2−x2+x3
 Coefficient of x2 is -1.
(iii) (π/2)x2 + x
Coefficient of x2 is (π/2)
(iv) √ 2  x −1
 There is no term consisting of x2. Therefore, coefficient of x2 is 0.
Question 3
Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Solution:
Degree of a polynomial is the highest power of variable in the polynomial.
Binomial has two terms in it. So binomial of degree 35 can be written as x35 + 1. Monomial has only one term in it. So monomial of degree 100 can be written as x100. Question 4.
Write the degree of each of the following polynomials:
(i) 5x3 + 4x2 + 7x
(ii) 4 – y2
(iii) 5t –√ 7
 (iv) 3
Solution:
(i) This is a polynomial in variable x and the highest power of variable x is 3 Therefore, the degree of this polynomial is 3.
(ii)This is a polynomial in variable y and the highest power of variable y is 2. Therefore, the degree of this polynomial is 2.
(iii) This is a polynomial in variable t and the highest power of variable t is 1. Therefore, the degree of this polynomial is 1.
(iv)This is a constant polynomial. Degree of a constant polynomial is always 0.
Question 5.
Classify the following as linear, quadratic and cubic polynomials:
(i) x2 + x
 (ii) x x3
(iii) y + y2 + 4
(iv) 1 + x
(v) 3t
(vi) r2
(vii) 7x3
Solution:
(i)       2 + x2 + x  is a quadratic polynomial as its degree is 2.
(ii)      x – x3 is a cubic polynomial as  its degree is 3.
(iii)     y + y2 + 4  is a quadratic polynomial as its degree is 2.
(iv)     1 + x is a linear polynomial as its degree is 1.
(v)      3t is a linear polynomial as its degree is 1.
(vi)     r2 is a quadratic polynomial as its degree is 2.
(vii)   7x3 is a cubic polynomial as its degree is 3.
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