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Class 10 Maths Important Questions for Polynomial





Given below are the Class 10 Maths Important Questions for Polynomial
a) Concepts questions
b) Calculation problems
c) Multiple choice questions
d) Long answer questions
e) Fill in the blank's
f) Match the column
Match the column
Degree of polynomial
Polynomial
1
x5 -3x2 +1
2
x-1
3
x4-3x2+2+ 3x3
4
x2 -2x-1
5
1-3x3
Match the column
type of polynomial
Polynomial
monomial
X3 -4x2 +1
binomial
x-1
trinomial
x4-3x2+2+ 3x3
No appropriate match
x2 -2
3x3
Table Type
P(x)=5x3 -3x2+7x+2
P(0)
P(1)
P(5)
P(-1)
P(-2)

Multiple choice Questions
  1. Find the remainder  when x4+x3-2x2+x+1 is divided by x-1
a)1
b)5
c)2
d)3
Solution ( c)
  1. Which of these identities is not true?
  1.  
  2.  
  3.  
  4.  
Solution (d)
True or False statement
  1. P(x) =x-1 and g(x) =x2-2x +1 .  p(x) is a factor of g(x)
  2. The factor of 3x2 –x-4 are  (x+1)(3x-4)
  3. Every linear polynomial has only one zero
  4. Every real number is the zero’s of zero polynomial
  5. A binomial may have degree 6
  6. 1,2 are the zeroes of x2-3x+2
  7. The degree of zero polynomial is not defined
  8.  Graph of polynomial (x2-1) meets the  x-axis at one point
  9. Graph of constant polynomial never meets x axis
Solution
  1. True, as g(1)=0
  2. True, we can get this by split method
  3. True
  4. True
  5. True , example x6 +1
  6. True
  7. True
  8. False as it meets at two points
  9.  True
Factorize following
  1. x2 +9x+18
  2. 3x3 –x2-3x+1
  3. x3-23x2+142x-120
  4. 1+8x3
Solution
a)     (x+6)(x+3)
b) )(3x-1)(x-1)(x+1)
c)(x-1)(x-10)(x-12)
d) (2x+1)(4x2-2x+1)
Match the column
Graph of polynomial
Number of Zeros

  0

  1

2

  3

  4

  5

  6

  7
Solution
a)  it cuts the x-axis at two points ,so 2 zeroes
b) it cuts the x-axis at four points ,so 4 zeroes
c) Since it does not cut the axis, so  0 zeroes
d) it cuts the x-axis at 1 points ,so 1 zero’s
e) it cuts the x-axis 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 x-axis 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
  1. If  and b are the zeroes of the polynomial  x2-11x +30, Find the value of a3 + b3
a)134
b)412
c)256
d)341
Solution
a3 + b3= (a+b) (a2+b2-ab)=(a+b) {(a+b)2 -3ab}
Now a+b=-(-11)/1=11
ab=30
So a3+b3=11( 121 -90)=341
  2) S(x) = px2+(p-2)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) x2-13x+22
b) x2-11x+22
c) x2-13x-22
d) x2+13x-22
Solution (a)
P(x) =(x-11)(x-2)
4) p(x) = x4 -6x3 +16x2 -25x +10
     q(x) = x2-2x+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
(2k-9)x –(8-k)k +10
Comparing this with (x+a)
We get
K=5 and a=-5
5) A cubic polynomial is given below
  S(x) =x3 -3x2+x+1
The zeroes of the polynomial are given as (p-q) ,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) =x4+x3+2x2+3x+4
     s(x) =x+2
b) p(x) =x4+4
  s(x)=x2+x+1
Solution
a) r(x)=x3-x2 +4x-5   w(x)=14
b) r(x)=x2-x  w(x) =x+4

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