**Hint:** Recall degree of polynomial in order to find the number of zeroes of polynomial.

**Question.1.** Which of the following statements is correct?

(a) A polynomial of degree 2 has three zeroes

(b) A polynomial of degree 3 has two zeroes

(c) A polynomial of degree 4 has four zeroes

(d) A polynomial of degree 5 has ten zeroes

**Question.2.** Ravi claims that the polynomial p(x)=mx^{a}+x^{2b} has 4b zeroes. For Ravi’s claim to be correct, which of these must be true?

(a) a = 2b or a = 4b

(b) a = 2 or a = 4b

(c) m = 2b

(d) m = 4b

**Ans.1.** (c) A polynomial of degree 4 has four zeroes**Ans.2.** (a) a = 2b or a = 4b

**Hint:** Analyse the graph of the polynomials in order to find the number of zeroes of polynomial.

**Question.3.** Which of the following graphs could be for the simple polynomial x^{2} ?

(a)

(b)

(c)

(d)

**Question.4.** Consider the expression x^{m^{2}-1}+3x^{\frac{m}{2}}, where m is a constant. For what value of m, will the expression be a cubic polynomial?

(a) -2

(b) -1

(c) 1

(d) 2

**Ans.3.** (b) **Ans.4.** (d) 2

**Hint:** Compute zeroes of the polynomials in order to verify the relationship between zeroes and the coefficients.

**Question.5.** Consider the polynomial in z, p(z)=z^{4}-2z^{3}+3. What is the value of the polynomial at z=-1?

(a) 2

(b) 3

(c) 5

(d) 6

**Question.6.** The polynomial in x, is x^{2}+kx+5, where k is a constant. At x=2, the value of the polynomial is 15.

What is the value of the polynomial at x=5?

(a) 3

(b) 18

(c) 35

(d) 45

**Ans.5.** (d) 6**Ans.6.** (d) 45

**Hint:** Compute the sum and product of zeroes of the polynomial in order to find the quadratic polynomial.

**Question.7.** Which of these is a zero of the polynomials P(y)=3y^{3}-16y-8?

(a) -8

(b) -2

(c) 0

(d) 2

**Question.8.** Given that m+2, where m is a positive integer, is a zero of the polynomial q(x)=x^{2}-mx-6.

Which of these is the value of m?

(a) 1

(b) 2

(c) 3

(d) 4

**Ans.7.** (b) -2**Ans.8.** (a) 1

**Hint:** Divide the two given polynomials in order to verify the division algorithm.

**Question.9.** The polynomial q(z)=z^{3}-4z+a when divided by the polynomial (z-3) leaves remainder 5. What is the value of a?

(a) –10

(b) –3

(c) 3

(d) 10

**Question.10.** The polynomial p(x)=x^{m}+x, where m>1, when divided by (x-a), leaves remainder 6. Given that a is a positive integer, what is the value of m?

(a) 2

(b) 3

(c) 5

(d) 6

**Ans.9.** (a) –10**Ans.10.** (a) 2

**Hint:** Divide the given polynomial with its known zero in order to find all the other zeroes of that polynomial.

**Question.11.** Which of these is a factor of the polynomial p(x)=x^{3}+4x+5 ?

(a) (x-1)

(b) (x+1)

(c) (x-2)

(d) (x+2)

**Question.12.** The polynomial (x-a), where a>0, is a factor of the polynomial q(x)=4\sqrt{2} x^{2}-\sqrt{2}. Which of these is a polynomial whose factor is (x-\frac{1}{a})?

(a) x^{2}+x+6

(b) x^{2}-5x+4

(c) x^{2}+4x-3

(d) x^{2}+x-6

**Ans.11.** (b) (x+1)**Ans.12.** (d) x^{2}+x-6