BASIC CONCEPTS IN POLYNOMIALS WORKSHEET

About "Basic Concepts in Polynomials Worksheet"

Basic Concepts in Polynomials Worksheet :

Here we are going to see some practice questions on basic concepts in polynomials.

Basic Concepts in Polynomials Worksheet - Questions

(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)x- 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)  3x+ 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 After having gone through the stuff given above, we hope that the students would have understood, "Basic Concepts in Polynomials Worksheet"

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