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Determine the value of k that will make (x−2) a factor of (x^4 + 3x^3 -8x^2 +kx +16)

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Ujjwal11id

Let, p (x) = x^4 + 3x^3 - 8x^2 + kx + 16

When, x = 2 then,

Using remainder theorem,

p(x) = x^4 + 3x^3 - 8x^2 + kx + 16

p(2) = 2^4 + 3*2^3 - 8*2^2 +k*2 + 16

0 = 16 + 3*8 - 8*4 + 2k + 16

0 = 16 + 24 - 32 + 2k + 16

0 = 24 + 2k

2k = -24

◆ k = -12

It is right answer...

I hope you understand...

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