BASIC CONCEPTS IN POLYNOMIALS WORKSHEET

(1)  Which of the following expressions are polynomials. If not give reason:

(i)  (1/x²) + 3x - 4

(ii)  x²(x - 1)

(iii)  (1/x)(x + 5)

(iv)  (1/x^-2) + (1/x^-1) + 7

(v)  √5 x² +  √3x + √2

(vi) m² - ∛m + 7m - 10              

Solution

(2)  Write the coefficient of x² and x in each of the following polynomials.

(i)  4 + (2/5)x² - 3x

(ii) 6 - 2x² + 3x³ - √7 x

(iii)  π x² - x + 2

(iv)  √3 x² + √2x + 0.5

(v)  x² - (7/2)x + 8 

Solution

(3)  Find the degree of the following polynomials.

(i)  1 - √2y² + y⁷

(ii)  (x³ - x⁴ + 6x⁶)/x²

(iii)  x³ (x² + x)

(iv)  3x⁴ + 9x² + 27x⁶ 

(v)  2√5p⁴ - (8p³/√3) + (2p²/7) 

Solution

(4)  Rewrite the following polynomial in standard form.

(i)  x - 9 + √7x³ + 6x²

(ii)   √2x² - (7/2)x⁴ + x - 5x³

(iii)   7x³ - (6/5)x² + 4x - 1

(iv)   y² - √5y³ - 11 - (7/3) y + 9y⁴              Solution

(5)  Add the following polynomials and find the degree of the resultant polynomial.

(i)  p(x)  =  6x² - 7x + 2 and q(x)  =  6x³ - 7x + 15

(ii)  h(x)  =  7x³ - 6x + 1, f(x)  =  7x² + 17x - 9

(iii)  f(x)  =  16x⁴ - 5x² + 9, g(x)  =  -6x³ + 7x - 15

Solution

(6)  Subtract the second polynomial from the first polynomial and find the degree of the resultant polynomial

(i)  p(x)  =  7x² + 6x - 1 and q(x)  =  6x - 9 

(ii)  f(y)  =  6y² - 7y + 2 and g(y)  =  7y + y³

(iii)  h(z)  =  z⁵ - 6z⁴ + z and f(z)  =  6z² + 10z - 7

Solution

(7)  What should be added to 2x³ + 6x² - 5x + 8 to get 3x³ - 2x² + 6x + 15 ?            Solution

(8)  What must be subtracted from 2x⁴ + 4x² - 3x + 7 to get 3x³ - x² + 2x + 1?            Solution

(9)  Multiply the following polynomials and find the degree of the resultant polynomial:

(i)  p(x)  =  x² - 9 and q(x)  =  6x² + 7x - 2

(ii)  f(x)  =  7x + 2 and g(x)  =  15x - 9 

(iii)  h(x)  =  6x² - 7x + 1 and f(x)  =  5x - 7

Solution

(10)  The cost of a chocolate is Rs. (x + y) and Amir bought (x + y) chocolates. Find the total amount paid by him in terms of x and y. If x = 10, y = 5 find the amount paid by him.              Solution

(11)  The length of a rectangle is (3x+2) units and it’s breadth is (3x–2) units. Find its area in terms of x. What will be the area if x = 20 units.              Solution

(12)  p(x) his a polynomial of degree 1 and q(x) is a polynomial of degree 2. What kind of the polynomial p(x) × q(x) is ?           Solution

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