**Basic Concepts in Polynomials Worksheet :**

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

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

(i) (1/x^{2}) + 3x - 4

(ii) x^{2}(x - 1)

(iii) (1/x)(x + 5)

(iv) (1/x^{-2}) + (1/x^{-1}) + 7

(v) √5 x^{2} + √3x + √2

(vi) m^{2} - ∛m + 7m - 10

(2) Write the coefficient of x^{2} and x in each of the following polynomials.

(i) 4 + (2/5)x^{2 }- 3x

(ii) 6 - 2x^{2} + 3x^{3} - √7 x

(iii) π x^{2} - x + 2

(iv) √3 x^{2} + √2x + 0.5

(v) x^{2} - (7/2)x + 8

(3) Find the degree of the following polynomials.

(i) 1 - √2y^{2} + y^{7}

(ii) (x^{3} - x^{4} + 6x^{6})/x^{2}

(iii) x^{3} (x^{2} + x)

(iv) 3x^{4 }+ 9x^{2} + 27x^{6}

(v) 2√5p^{4} - (8p^{3}/√3) + (2p^{2}/7)

(4) Rewrite the following polynomial in standard form.

(i) x - 9 + √7x^{3} + 6x^{2}

(ii) √2x^{2} - (7/2)x^{4} + x - 5x^{3}

(iii) 7x^{3} - (6/5)x^{2} + 4x - 1

(iv) y^{2} - √5y^{3} - 11 - (7/3) y + 9y^{4 }Solution

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

(i) p(x) = 6x^{2} - 7x + 2 and q(x) = 6x^{3} - 7x + 15

(ii) h(x) = 7x^{3} - 6x + 1, f(x) = 7x^{2} + 17x - 9

(iii) f(x) = 16x^{4} - 5x^{2} + 9, g(x) = -6x^{3} + 7x - 15

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

(i) p(x) = 7x^{2} + 6x - 1 and q(x) = 6x - 9

(ii) f(y) = 6y^{2} - 7y + 2 and g(y) = 7y + y^{3}

(iii) h(z) = z^{5} - 6z^{4} + z and f(z) = 6z^{2} + 10z - 7

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

(8) What must be subtracted from 2x^{4} + 4x^{2} - 3x + 7 to get 3x^{3} - x^{2} + 2x + 1? Solution

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

(i) p(x) = x^{2} - 9 and q(x) = 6x^{2} + 7x - 2

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

(iii) h(x) = 6x^{2} - 7x + 1 and f(x) = 5x - 7

(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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