Question

19. If (x - 2) is a factor of x4 - 16 then find the remainder.
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Answer 1

If it is factor then remainder toh 0 hi aaega....

Answer 2

Answer:

$\red { Required \: remainder }$

$\green {= x^{3} + 2x^{2} + 4x + 8}$

Step-by-step explanation:

$Given \: (x-2) \:is \: a \: factor \: of \: x^{4} - 16$

$Remainder = \frac{x^{4} - 16 }{(x-2)}\\= \frac{(x^{2})^{2} - 4^{2}}{(x-2)} \\= \frac{(x^{2}+4)(x^{2}-4)}{(x-2)}$

$= \frac{(x^{2}+4)(x^{2} - 2^{2})}{(x-2)}\\= \frac{(x^{2}+4)(x+2)(x-2)}{(x-2)}\\= (x^{2}+4)(x+2) \\= x^{3} + 2x^{2} + 4x + 8$

Therefore.,

$\red { Required \: remainder }$

$\green {= x^{3} + 2x^{2} + 4x + 8}$

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