Mixed Problems on Adding and Subtracting Polynomials :
In this section, you will learn, how to add and subtract 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
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
f(y) - g(y) = (6y2 - 7y + 2) - (7y + y3)
= 6y2 - 7y + 2 - 7y - y3
= - y3 + 6y2 - 7y - 7y + 2
= - y3 + 6y2 - 14y + 2
Degree of the resultant polynomial is 3.
(iii) h(z) = z5 - 6z4 + z and f(z) = 6z2 + 10z - 7
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 ?
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?
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 - 3x3 + 4x2 + x2 - 3x - 2x + 7 - 1
p(x) = 2x4 - 3x3 + 5x2 - 5x + 6
After having gone through the stuff given above, we hope that the students would have understood, how to add and subtract polynomials.
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