Class 10 Maths Problems for Polynomials

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

Question 1
Verify that 3, -1, -1/3 are the zeroes of the cubic polynomial $p(x)=3x^3-5x^2-11x-3$

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

Question 4
Using division state whether $2y - 5$ is a factor of $4y^4 - 10y^3 - 10y^2 + 30y - 15$.

Question 5
Check whether $g(x) = x^2 - 3$ is a factor of $p(x) = 2x^4 + 3x^3 - 2x^2 - 9x -12$ by applying division algorithm.

Question 6
Check whether $p(x) = x^2 +3x +1$ is a factor of $g(x) = 3x^4+ 5x^3 - 7x^2+ 2x + 2$ by using division algorithm.

Question 7
Find remainder when $x^3 - bx^2 + 5- 2b$ is divided by $x - b$.

Question 8
Check whether polynomial $x - 3$ is a factor of the polynomial $x^3 - 3x^2 - x + 3$. Verify by division algorithm.

Question 9
If $4x^4 + 7x^3 - 4x^2 - 7x + p$ is completely divisible by $x^3 - x$, then find the value of p.

Question 10
If α and β are the zeroes of the quadratic polynomial $f(x) = kx^2 + 4x + 4$ such that α2 + β2 = 24, find the values of k.

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

Question 12
If the squared difference of the zeroes of the quadratic polynomial
$f(x) = x^2 + px + 45$ is equal to 144, find the value of p.

Question 13
If α and β are the zeroes of the quadratic polynomial $f(x) = x^2 - p (x + 1) - c$, show that (α + 1) (β + 1) = 1 – c.

Question 14
What must be subtracted from the polynomial $f(x) = x^4 + 2x^3 - 13x^2- 12x + 21$
so that the resulting polynomial is exactly divisible by $x^2 - 4x + 3$?

Question 15
Verify that 1, 2 and -1/2 are zeroes of $2x^3 - 5x^2 + x + 2$. Also verify the relationship between the zeroes and the coefficients.
Question 16 On dividing the polynomial $4x^4 - 5x^3 - 39x^2 -46x- 2$ by the polynomial g(x), the quotient is $x^2 - 3x -5$ 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.

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Practice Question

Question 1 What is $1 - \sqrt {3}$ ?
A) Non terminating repeating
B) Non terminating non repeating
C) Terminating
D) None of the above
Question 2 The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is?
A) 19.4 cm3
B) 12 cm3
C) 78.6 cm3
D) 58.2 cm3
Question 3 The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?
A) 2 ,21,11
B) 1,10,19
C) -1 ,8,17
D) 2 ,11,20