Telangana SCERT Solution Class IX (9) Math Chapter 2 Polynomials and Factorisation Exercise 2.1
(1) (i) x5 – x4 + 3
The highest power of the 3 terms is 5.
So, the degree of the above polynomial is 5.
(ii) x2 + x – 5
The highest power of the 3 terms is 2.
∴ The degree of the polynomial is 2.
(iii) 5
Now, 5 can be written as 5x0 (∵ x0 = 1)
∴ The degree of the polynomial is 0.
(iv) 3x6 + 6y3 – 7
The degree of the polynomial is 6.
(v) 4 – y2
The degree of the polynomial is 2,
(vi) 5t – √3
The degree of the polynomial is 1.
(2) (i) 3x2 – 2x + 5 is one variable polynomial since the only variable in the polynomial is x.
(ii) x2 + √2 is one variable polynomial since the only variable in the polynomial is x.
(iii) P2 – 3p + q is a two variable polynomial since there are two variable p and q in the polynomial.
(iv) y + 2/y is a one variable polynomial since there are is only one variable ‘y’ in the polynomial.
(v) 5√x + x√5 is a one variable polynomial since there is only one variable ‘x’ in the polynomial.
(vi) x100 + y100 is a two variable polynomial as there are two variables x and y in the polynomial.
(3) (i) x3 + x + 1
Coefficient of x3 is 1.
(ii) 2 – x3 + x2
Coefficient of x3 is -1
(iii) √2x3 + 5
Coefficient of x3 is √2
(iv) 2x3 + 5
Coefficient of x3 is 2.
(v) π/2 x3 + x
Coefficient of x3 is π/2
(vi) -2/3 x3
Coefficient of x3 is -2/3
(vii) 2x2 + 5 ‘
or, 2x2 + 5 + 0 X x3
Coefficient of x3 is 0.
(viii) 4
Or, 0 X x3 + 4
Coefficient of x3 is 4
(4) (i) 5x2 + x – 7 is a quadratic polynomial having highest degree 2.
(ii) x – x3 is a cubic polynomial having highest degree 3.
(iii) x2 + x + 4 is a quadratic polynomial having highest degree 2.
(iv) x – 1 is linear polynomial having highest degree 1
(v) 3p is a linear polynomial having highest degree 1.
(vi) πr2 is a quadratic polynomial having highest degree 2.
(5.) (i) A binomial has two terms
Ans. True.
(ii) Every polynomial is a binomial
Ans. False.
(iii) A binomial may have degree 3
Ans. True.
(iv) Degree of zero polynomial is zero
Ans. False.
(v) The degree of x2 + 2xy + y2 is 2
Ans. True.
(vi) πr2 is a monomial
Ans. True.
(6) Monomial of degree 10 is 4x10
Trinomial of degree 10 is 5x10 + x6 + 3.
Thank you but in 5th bit u should justify