- Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) 4x2 – 3x + 7
(ii) y2 + √2
(iii) 3√t + t√2
(iv) y + 2/y
(v)x10 +y3 + t50
Solution:
(i)Polynomial in one variable, x
(ii)Polynomial in one variable, y
(iii) 3√t + t√2 is not a polynomial as power of t in √2t is not a whole number
(iv) y + 2/y is not a polynomial as a power of y in 1/y = y-1 is not a whole number
(v) x10 +y3 + t50 is not a polynomial with three variables x , y and t.
- Write the coefficients of x2 in each of the following:
(i) 2+ x2 + x
(ii) 2 – x2 + x3
(iii) π/2 . x2 + x
(iv)√2x – 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)√2x – 1, x2 is not there therefore there is no coefficient.
- Give one example each of a binomial of degree 35 and of a monomial of degree 100
Solution:
Binomial of degree 35 can be a35 + 10
monomial of degree 100 can be x100
- Write the degree of each of the following polynomials:
(i) 5x3 + 4x2+ 7
(ii) 4 – y2
(iii) 5t – √7
(iv) 3
Solution:
(i) 5x3 + 4x2+ 7, degree of a polynomial is 3 as x3 is the highest power.
(ii) 4 – y2, degree of a polynomial is 2 as x2 is the highest power.
(iii) 5t – √7, degree of a polynomial is 1 as x is the highest power.
(iv) 3, degree of a polynomial is 0 as x0 is the highest power.
- 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)x2 + x, is quadratic
(ii) x – x3, , is cubic
(iii)y + y2 + 4, is quadratic
(iv) 1 + x, is linear
(v) 3t, is linear
(vi) r2, is quadratic
(vii) 7x3, is cubic
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