SUBTRACTION OF POLYNOMIALS

Question 1 :

Subtract the second polynomial from the first polynomial and find the degree of the resultant polynomial

(i)  p(x)  =  7x2 + 6x - 1 and q(x)  =  6x - 9 

Solution :

p(x) - q(x)  =  (7x2 + 6x - 1) - (6x - 9)

  =  7x2 + 6x - 1 - 6x + 9

  =  7x2 + 6x - 6x  - 1 + 9

  =  7x2 + 8

Degree of the resultant polynomial is 2.

(ii)  f(y)  =  6y2 - 7y + 2 and g(y)  =  7y + y3

Solution :

f(y) - g(y)  =  (6y2 - 7y + 2) - (7y + y3)

  =  6y2 - 7y + 2 - 7y - y3

  =  - y+ 6y2 - 7y - 7y + 2

  =  - y+ 6y2 - 14y + 2

Degree of the resultant polynomial is 3.

(iii)  h(z)  =  z5 - 6z4 + z and f(z)  =  6z2 + 10z - 7

Solution :

h(z) - f(z)  =  (z5 - 6z4 + z) - (6z2 + 10z - 7)

  =  z5 - 6z4 + z - 6z2 - 10z + 7

  =  z5 - 6z4 - 6z2 - 9z + 7

Degree of the resultant polynomial is 5.

Question 2 :

What should be added to 2x3 + 6x2 - 5x + 8 to get 3x3 - 2x2 + 6x + 15 ?

Solution :

Let p(x) be the required polynomial to be added

By adding p(x) and 2x3 + 6x2 - 5x + 8, we will get 3x3 - 2x2 + 6x + 15

p(x) + (2x3 + 6x2 - 5x + 8)  =  3x3 - 2x2 + 6x + 15

p(x)  =  (3x3 - 2x2 + 6x + 15) - (2x3 + 6x2 - 5x + 8)

p(x)  =  3x3 - 2x3- 2x2 + 6x2  + 6x - 5x + 15 + 8

p(x)  =  x3 + 4x2 + x + 23

Question 3 :

What must be subtracted from 2x4 + 4x2 - 3x + 7 to get 3x3 - x2 + 2x + 1?

Solution :

Let p(x) be the required polynomial to be subtracted.

 (2x4 + 4x2 - 3x + 7) - p(x)  =  3x3 - x2 + 2x + 1

p(x)  =  (2x4 + 4x2 - 3x + 7) - (3x3 - x2 + 2x + 1)

  =  2x4 + 4x2 - 3x + 7 - 3x3 + x2 - 2x - 1

  =  2x4 - 3x+ 4x2 + x- 3x - 2x + 7 - 1

p(x)  =  2x4 - 3x+ 5x2 - 5x + 6

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