Q. 5

Taking p(x) = 3x2 – 2x + 4, write the following as polynomials:

i) (x + 1) p(x) + (x – 1) p(x)

ii) (x + 1) p(x) – (x – 1) p(x)

iii)

Answer :

(i) p(x) = 3x2 – 2x + 4

Now,


(x + 1) p(x) + (x – 1) p(x)


taking p(x) common


p(x)[x + 1 + x-1]


2x × p(x)


2x × (3x2 – 2x + 4)


6x3 – 4x2 + 8x


(ii) p(x) = 3x2 – 2x + 4


Now,


(x + 1) p(x) - (x – 1) p(x)


taking p(x) common


p(x)[x + 1-x + 1]


2 × p(x)


2 × (3x2 – 2x + 4)


6x2 – 4x + 8


(iii) p(x) = 3x2 – 2x + 4


Now,



taking p(x) common



p(x)


3x2 – 2x + 4


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