which of the expressions are polynomials? which r not? 1)4x²+3/x-5. 2)5. 3)3xyz. 4)y²-8. 5)1/x+1. 6)√3x²-5y. 7)√x. 8)3xyz
Answers
Answer:
Step-by-step explanation:
1. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
Ans. (i) 4x2 – 3x + 7
⇒ 4x2 – 3x + 7x°
∵ All the exponents of x are whole numbers.
∴ 4x2 – 3x + 7 is a polynomial in one variable.
(ii)
∵ All the exponents of y are whole numbers.
∴ is a polynomial in one variable.
(v) x10 + y3 + t50
∵; Exponent of every variable is a whole number,
∴ x10 + y3 + t50 is a polynomial in x, y and t, i.e. in three variables.
2. Write the co-efficients of x2 in each of the following:
(i) 2 + x2 + x (ii) 2 – x2 + x3 (iii) (v)
Ans. (i) 2 + x2 + x
The co-efficient of x2 is 1.
(ii) 2 – x2 + x3
The co-efficient of x2 is (–1).
(iii)
The co-efficient of x2 is
(iv)
∴ The co-efficient of x2 is 0
3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Ans. (i) A binomial of degree 35 can be: 3x35 – 4
(ii) A monomial of degree 100 can be:
4. Write the degree of each of the following polynomials:
(i) 5x3 + 4x2 + 7x (ii) 4 - y2 (iii) (iv) 3
Ans. (i) 5x3 + 4x2 + 7x
∵ The highest exponent of x is 3.
∴ The degree of the polynomial is 3.
(ii) 4 – y2
∵ The highest exponent of y is 2.
∴ The degree of the polynomial is 2.
(iii)
∵ The highest exponent of t is 1.
∴ The degree of the polynomial is 1.
(iv) 3
since, 3 = 3x°
∴ The degree of the polynomial 3 is 0.
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
Ans. (i) x2 +x
∵ The degree of x2 + x is 2.
∴ It is a quadratic polynomial.
(ii) x – x3
∵ The degree of x – x3 is 3.
∴ It is a cubic polynomial.
(iii) y + y2 + 4
∵ The degree of y + y2 + 4 is 2.
∴ It is a quadratic polynomial.
(iv) 1 + x
∵ The degree of 1 + x is 1.
∴ It is a linear polynomial.
(v) 3t
∵ The degree of 3t is 1.
∴ It is a linear polynomial.
(vi) r2
∵ The degree of r2 is 2.
∴ It is a quadratic polynomial.
(vii) 7x3
∵ The degree of 7x3 is 3.
∴ It is a cubic polynomial.
Answer:
1 to 5
Step-by-step explanation:
(i) and (ii) are polynomials is one-variable (iii) is not polynomial (iv) is not a polynomial (v) is a polynomial in three variables.