1. Which one of the following is a polynomial? 2. √2 is a polynomial of degree (A) 2 (B) 0 (C) 1 (D) ½ 3. Degree of the polynomial 4×4 + 0x3 + 0x5 + 5x + 7 is (A) 4 (B) 5 (C) 3 (D) 7 4. Degree of the zero polynomial is (A) 0 (B) 1 (C) Any natural number (D) Not defined 5. If p(x)= x2 – 2√2x + 1, then p(2√2) is equal to (A) 0 (B) 1 (C) 4√2 (D) 8√2 +1 6. The value of the polynomial 5x – 4x2 + 3, when x = – 1 is (A) – 6 (B) 6 (C) 2 (D) – 2 7. If p(x) = x + 3, then p(x) + p(–x) is equal to (A) 3 (B) 2x (C) 0 (D) 6 8. Zero of the zero polynomial is (A) 0 (B) 1 (C) Any real number (D) Not defined 9. Zero of the polynomial p(x) = 2x + 5 is (A) – 2/5 (B) – 5/2 (C) 2/5 (D) 5/2 10. One of the zeroes of the polynomial 2x2 + 7x –4 is (A) 2 (B) ½ (C) – ½ (D) –2 Exercise - 2.2 1. Which of the following expressions are polynomials? Justify your Exercise - 2.3 1. Classify the following polynomials as polynomials in one variable, two variables etc. (i) x2 + x + 1 (ii) y3 – 5y (iii) xy + yz + zx (iv) x2 – 2xy + y2 + 1 2. Determine the degree of each of the following polynomials: (i) 2x – 1 (ii) –10 (iii) x3 – 9x + 3x5 (iv) y3 (1 – y4) 3. For the polynomial (i) the degree of the polynomial (ii) the coefficient of x3 (iii) the coefficient of x6 (iv) the constant term 4. Write the coefficient of x2 in each of the following: (i) (π/6)x + x2 – 1 (ii) 3x – 5 (iii) (x –1) (3x – 4) (iv) (2x – 5) (2x2 – 3x + 1) 5. Classify the following as a constant, linear, quadratic and cubic polynomials: (i) 2 – x2 + x3 (ii) 3x3 (iii) 5t – √7 (iv) 4 – 5y2 (v) 3 (vi) 2 + x (vii) y3 – y (viii) 1 + x + x2 (ix) t2 (x) √2x – 1 6. Give an example of a polynomial, which is: (i) monomial of degree 1 (ii) binomial of degree 20 (iii) trinomial of degree 2 7. Find the value of the polynomial 33 – 42 + 7 – 5, when x = 3 and also when x = –3. 8. If p() =2 – 4 + 3, evaluate: (2)− (−1) + (½). 9. Find p(0), p(1),(−2) for the following polynomials: (i) ()=10−42 –3 (ii) ()=(y + 2) (y – 2) 10. Verify whether the following are true or false: (i) –3 is a zero of x – 3 (ii) – 1/3 is a zero of 3x + 1 (iii) – 4/5 is a zero of 4 –5y (iv) 0 and 2 are the zeroes of t2 – 2t (v) –3 is a zero of y2 + y – 6 11. Find the zeroes of the polynomial in each of the following: (i) p(x) = x – 4 (ii) g(x) = 3 – 6x (iii) q(x) = 2x –7 (iv) h(y) = 2y 12. Find the zeroes of the polynomial: p()= ( –2)2−( + 2)2 13. By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x4 + 1; x –1 14. By Remainder Theorem find the remainder, when p(x) is divided by g(x), where (i) p() = 3 – 22 – 4 – 1, g() = + 1 (ii) p() = 3 – 32 + 4 + 50, g() = – 3 (iii) p() = 43 – 122 + 14 – 3, g() = 2 – 1 (iv) p() = 3 – 62 + 2 – 4, g() = 1 – 3/2 15. Check whether p() is a multiple of g() or not: (i) p() = 3 – 52 + 4 – 3, g() = – 2 (ii) p()= 23 – 112− 4 + 5, ()= 2 + 1 16. Show that: (i) + 3 is a factor of 69 + 11−2 + 3. (ii) 2−3 is a factor of + 23 – 92 + 12 17. Determine which of the following polynomials has x – 2 a factor: (i) 32 + 6−24. (ii) 42 + −2. 18. Show that p – 1 is a factor of p10 – 1 and also of p11 – 1. 19. For what value of m is 3 – 22 + 16 divisible by x + 2? 20. If + 2 is a factor of 5 – 423 + 2 + 2 + 3, find a. Exercise 2.4 1. If the polynomials az3 + 4z2 + 3z – 4 and z3 – 4z + a leave the same remainder when divided by z – 3, find the value of a. 2. The polynomial p(x) = x4 – 2x3 + 3x2 – ax + 3a – 7 when divided by x + 1 leaves the remainder 19. Find the values of a. Also find the remainder when p(x) is divided by x + 2. 3. If both x – 2 and x – ½ are factors of px2 + 5x + r, show that p = r. 4. Without actual division, prove that 2x4 – 5x3 + 2x2 – x + 2 is divisible by x2 – 3x + 2. [Hint: Factorise x2 – 3x + 2]