Question

(5)Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(ii) (2x3 - 2x2 + ax – a) ; (x – a)
PLEASE ANSWER THIS ​

Answer 1

Step-by-step explanation:

p(x) = 2x3 – 2x2 + ax – a

Divisor = x – a

∴ take x = a

By remainder theorem,

Remainder = p(a)

p(x) = 2x3 – 2x2 + ax – a

∴ p(a) = 2a3 – 2a2 + a(a) – a

= 2a3 – 2a2 + a2 – a

∴ Remainder = 2a3 – a2 – a

Answer 2

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$\sf{p(x) = 2x3 – 2x2 + ax – a}$

$\sf{Divisor = x – a}$

$\sf{∴ take ~x = a}$

By remainder theorem,

$\sf{Remainder = p(a)}$

$\sf{p(x) = 2x3 – 2x2 + ax – a}$

$\sf{∴ p(a) = 2a3 – 2a2 + a(a) – a}$

$\sf{= 2a3 – 2a2 + a2 – a}$

$\sf{∴ Remainder = 2a3 – a2 – a}$