Given below are the Class 10 Maths Important Questions for Polynomial
a) Concepts questionsMatch the column
Degree of polynomial 
Polynomial 
1 
x^{5} 3x^{2} +1 
2 
x1 
3 
x^{4}3x^{2}+2+ 3x^{3} 
4 
x^{2} 2x1 
5 
13x^{3} 
Match the column
type of polynomial 
Polynomial 
monomial 
X^{3} 4x^{2} +1 
binomial 
x1 
trinomial 
x^{4}3x^{2}+2+ 3x^{3} 
No appropriate match 
x^{2} 2 

3x^{3} 
Table Type
P(x)=5x^{3} 3x^{2}+7x+2
P(0) 
P(1) 
P(5) 
P(1) 
P(2) 





Multiple choice Questions
a)1
b)5
c)2
d)3
Solution ( c)
Solution (d)
True or False statement
Solution
Factorize following
Solution
a) (x+6)(x+3)
b) )(3x1)(x1)(x+1)
c)(x1)(x10)(x12)
d) (2x+1)(4x^{2}2x+1)
Match the column
Graph of polynomial 
Number of Zeros 
0 

1 

2 


3 

4 

5 

6 

7 
Solution
a) it cuts the xaxis at two points ,so 2 zeroes
b) it cuts the xaxis at four points ,so 4 zeroes
c) Since it does not cut the axis, so 0 zeroes
d) it cuts the xaxis at 1 points ,so 1 zero’s
e) it cuts the xaxis at 1 points ,so 1 zero’s
f) Since it does not cut the axis, so 0 zeroes
g) Since it does not cut the axis, so 0 zeroes
h) it cuts the xaxis at two points ,so 2 zeroes
Match the column
Graph of polynomial 
Type of polynomial 

Linear polynomial 

Quadratic polynomial 

Cubic polynomial 

Constant polynomial 








Solution
a) Quadratic as parabola
b) Three zeroes,So cubic polynomial
c) Contant value polynomial
d) Linear polynomial
e) One zeroes but not straight line. So no appropriate match found
f) Quadratic as parabola
g) Quadratic as parabola
e) Cubic as has three zeroes ,two of them same
Multiple Choice Questions
a)134
b)412
c)256
d)341
Solution
a^{3} + b^{3}= (a+b) (a^{2}+b^{2}ab)=(a+b) {(a+b)^{2} 3ab}
Now a+b=(11)/1=11
ab=30
So a^{3}+b^{3}=11( 121 90)=341
2) S(x) = px^{2}+(p2)x +2. If 2 is the zero of this polynomial,what is the value of p
a)1
b)1/2
c) 1/2
d)+1
Solution
S(2)=4p+0+2=0 => p=1/2
3) if the zeroes of the quadratic equation are 11 and 2 ,what is expression for quadratic
a) x^{2}13x+22
b) x^{2}11x+22
c) x^{2}13x22
d) x^{2}+13x22
Solution (a)
P(x) =(x11)(x2)
4) p(x) = x^{4} 6x^{3} +16x^{2} 25x +10
q(x) = x^{2}2x+k
It is given
p(x) = r(x) q(x) + (x+a)
Find the value of k and a
a) 2,2
b) 5 ,5
c) 7,3
d) 3,1
Solution (b)
Dividing p(x) by q(x) ,we get the remainder
(2k9)x –(8k)k +10
Comparing this with (x+a)
We get
K=5 and a=5
5) A cubic polynomial is given below
S(x) =x^{3} 3x^{2}+x+1
The zeroes of the polynomial are given as (pq) ,p and (p+q). What is the value p and q
a) 1 ,
b) 1,2
c) 1,2
d) None of these
Solution (a)
Division of polynomial
s(x) =r(x) s(x) + w(x)
Find the value of r(x) and w(x) in each case
a) p(x) =x^{4}+x^{3}+2x^{2}+3x+4
s(x) =x+2
b) p(x) =x^{4}+4
s(x)=x^{2}+x+1
Solution
a) r(x)=x^{3}x^{2} +4x5 w(x)=14
b) r(x)=x^{2}x w(x) =x+4