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) $$2 ( x - 1 )( x^2 - 1)$$