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/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
(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
(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)
(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
(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
(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
(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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