Math, asked by parth0955, 1 year ago

what is the remainder when(x4 +1) is divided by (x-2)

Answers

Answered by Anshik78

Hey mate here is ur answer. .....

when we devided 4x+1 from x-2 then reminder is 9

I hope its help you!!!!

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Anshik78: hmm

shadowsabers03: It's 1 - (- 16) = 1 + 16 = 17

Anshik78: maine anwer me ek pic add ki h dekh lo

shadowsabers03: There's a wrong at first step. x - 2 when multiplied by x^3 gives x^4 - 2x^3. When this x^4 - 2x^3 is subtracted, 'x^4' in x^4 - 2x^3 is subtracted from 'x^4' in x^4 + 1 and '- 2x^3' in 'x^4 - 2x^3 is subtracted from '0x^3' in x^4 + 1. Therefore, we get (x^4 + 0x^3) - (x^4 - 2x^3) = x^4 + 0x^3 - x^4 + 2x^3 = 2x^3. But you wrote - 2x^3 there, at first step.

shadowsabers03: Also, the same error is occurred in the second, third and fourth steps.

shadowsabers03: It's,

shadowsabers03: 0x^2 - ( -4x^2) = 0x^2 + 4x^2 = 4x^2

shadowsabers03: 0x - ( -8x) = 0x + 8x = 8x

shadowsabers03: and 1 - ( -16) = 1 + 16 = 17

shadowsabers03: The quotient obtain is x^3 + 2x^2 + 4x + 8, not x^3 - 2x^2 - 4x - 8.

Answered by shadowsabers03

Answer:

$\bold{17}$

Step-by-step explanation:

$x^4 + 1 \\ \\ = x^4 - 2x^3 + 2x^3 - 4x^2 + 4x^2 - 8x + 8x - 16 + 17 \\ \\ = x^3(x - 2) + 2x^2(x - 2) + 4x(x - 2) + 8(x - 2) + 17 \\ \\ = (x - 2)(x^3 + 2x^2 + 4x + 8) + \bold{17} \\ \\ \\ $This means that$\ x^4 + 1\ $when divided by$\ x - 2\ $gives quotient$\ x^3 + 2x^2 + 4x + 8\ $and remainder$\ 17. \\ \\ \\ \therefore\ $The remainder is$\ \bold{17}. \\ \\ \\$

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