Class 09 - Chapter 02 - Polynomials (10)

Posted in Class IX

Q.1. State whether the following expression is a polynomial or not:

(a) \( 3x \)       (b) \( \frac{3}{y} \)     (c) \( \sqrt{2x} - 5 \)     (d) \( 32 - x^2 \)      (e) \( \sqrt{2}x - 6 \)

(f) \( y^2 - y + y^{-1} \)

Q.2. Find the degree of each of the following polynomials given below:

(a) \( x^2 + 2x + 4 \)     (b) \(x^2 + x^7 - 2 x^3 + 1 \)    (c) \( x^2y^2 - xy - 3\)     (d) \( 1 - 3 x - 4 x^3 \)

Q.3. Find the coefficient of each term in the following polynomials:

(a) \( -3x^3 \)   (b) \( x^7 - 2x^6 + 12x^3 \)

Q.4. Identify the type of polynomial (linear, quadratic, cubic) from among the following polynomials:

(a) \( 3 - 4x^3 \)        (b) \( y - 2y^2 + 4 \)       (c) \( y - 3 \)        (d) \( 3y^2 - 5y^3 + 6 \)

(e) \( 2( 3 - y) \)        (f) \( y ( y - 3 ) -y^2 \)      (g) \( y^2 ( y - 3) \)      (h) \( 2 - 2 (y - 2) + y^3 \)

Q.5. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

(a) \( -3x + 7 \)     (b) \( y + \sqrt{3} \)     (c) \( \sqrt{3} - y^2 + 3 \)    (d) \( 4 \sqrt{y^2 - 1} - 6 \sqrt{3} \)

Q.6. Write the coefficient of \(x^2\) in each of the following:

(a) \( -2 x^2 + 3 \)      (b) \( 1 + x - x^2 \)    (c) \( 7 + x ( 7 - x ) \)    (d) \( \frac{\sqrt{3} + 1}{2} x^2 + 7x - 21 \)

Q.7. Write the degree of each of the following polynomials:

(a) \( x^6 - 1 \)     (b) \( \frac{\sqrt{3}}{2} x^3 - \frac{1}{2} x^2 + x - 1 \)     (c) \( 7y - 1 \)    (d) 21     (e) 12

Q.8. Classify the following as linear, quadratic and cubic polynomials:

(a) \( x - x^3 \)     (b) \( 25x^2 - 15x + 5 \)       (c) \( 1 - x \)     (d) \( 5r^3 \)        (e) \( 7y \)    (f) \( x ( x + 1 ) - x^2 \)

Q.9.Write the coefficient of \( x^3 \) in each of the following:

(a) 1    (b) \( x ( 1 - x^2) + 3 x^2 \)    (c) \( x - 2x ( x^2 - 6 ) - 6x^3 \)   (d) \( \frac{1}{2} x^3 + \frac{3}{4} x^3 \)

Q.10. Write the degree of each of the following polynomials:

(a) \( (x - 1) (x + 1) \)     (b) \( (x + 1)(x^2 + x + 1) \)     (c) \( (x^2 - 1)(x^2 + 1) \)    (d) \( 2 ( x - 1 )( x^2 - 1) \)