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)

(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