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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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