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Class 10 Maths Problems for Polynomials





Given below are the Class 10 Maths Problems for Polynomials with solutions
a) cubic polynomials problems
b) quadratic polynomials Problems
c) Word Problems

Question 1 Verify that 3, -1, -1/3  are the zeroes of the cubic polynomial p(x)=3x3-5x2-11x-3

Question 2 Verify that -5,1/2,3/4 are zeroes of cubic polynomial 4y3 + 20y + 2y -3. Also verify the relationship between the zeroes and the coefficients.
Question 3 Using division show that 3x2 + 5 is a factor of 6x5 + 15x4 + 16x3 + 4x2 + 10x – 35.

Question 4 Using division state whether 2y – 5 is a factor of 4y4 – 10y3 – 10y2 + 30y – 15.
Question 5 Check whether g(x) = x2 – 3 is a factor of p(x) = 2x4 + 3x3 – 2x2 – 9x – 12 by applying division algorithm.
Question 6 Check whether p(x) = x2 +3x +1 is a factor of g(x) = 3x4 + 5x2 – 7x2 + 2x + 2 by using division algorithm.
Question 7 Find remainder when x3 – bx2 + 5 – 2b is divided by x – b.

Question 8 Check whether polynomial x – 3 is a factor of the polynomial x3 – 3x2 – x + 3. Verify by division algorithm.
Question 9 If 4x4 + 7x3 – 4x2 – 7x + p is completely divisible by x3 – x, then find the value of p.
Question 10 If α and β are the zeroes of the quadratic polynomial f(x) = kx2 + 4x + 4 such that α2 + β2 = 24, find the values of k.

Question 11 If α and β are the zeroes of the quadratic polynomial f(x) = 2x2 – 5x + 7, find a polynomial whose zeroes are 2α + 3β and 3α + 2β.


Question 12 If the squared difference of the zeroes of the quadratic polynomial
f(x) = x2 + px + 45 is equal to 144, find the value of p.

Question 13 If α and β are the zeroes of the quadratic polynomial f(x) = x2 – p (x + 1) – c, show that (α + 1) (β + 1) = 1 – c.

Question 14 What must be subtracted from the polynomial f(x) = x4 + 2x3 – 13x2 – 12x + 21
so that the resulting polynomial is exactly divisible by x2 – 4x + 3?
Question 15 Verify that 1, 2 and -1/2 are zeroes of 2x3 – 5x2 + x + 2. Also verify the relationship between the zeroes and the coefficients.
Question 16 On dividing the polynomial 4x4 – 5x3 – 39x2 – 2 by the polynomial g(x), the quotient is x2 – 3x -5 and the remainder is -5x + 8. Find the polynomial g(x).
Question 17 If α and β are the zeroes of the polynomial f(x) = x2 + px + q, form a polynomial whose zeroes are (α + β)2 and (α – β)2.

Question 18 On dividing the polynomial 4x4 – 5x3 – 39x2 – 2 by the polynomial g(x), the quotient and remainder were x2 – 3x – 5 and -5x + 8 respectively. Find g(x).


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Reference Books for class 10

Given below are the links of some of the reference books for class 10 math.

  1. Oswaal CBSE Question Bank Class 10 Hindi B, English Communication Science, Social Science & Maths (Set of 5 Books)
  2. Mathematics for Class 10 by R D Sharma
  3. Pearson IIT Foundation Maths Class 10
  4. Secondary School Mathematics for Class 10
  5. Xam Idea Complete Course Mathematics Class 10

You can use above books for extra knowledge and practicing different questions.


Class 10 Maths Class 10 Science

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