anonymous
  • anonymous
How do we find the value of k?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[(3x+k)^3 + (4x-7)^2 \]
anonymous
  • anonymous
has a remainder of 33 when divided by (x-3), how do we find the value of k?
A_clan
  • A_clan
(3x+k)3+(4x−7)2 + 33 ---------------------- = some Integer , say I (x-3)

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More answers

anonymous
  • anonymous
why did you add 33 to the expression?
A_clan
  • A_clan
Because 33 remained when we divided the expression by (x-3). So adding it to the expression will cause the expression to be completely divisible by (x-3).
A_clan
  • A_clan
Sorry, it had to be subtracted.
anonymous
  • anonymous
:o yeah
A_clan
  • A_clan
(3x+k)3+(4x−7)2 - 33 ---------------------- = some Integer , say I (x-3)
anonymous
  • anonymous
whats \[(3x+k)^3 ?\]
A_clan
  • A_clan
Expanding it is the only way it seems. (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
anonymous
  • anonymous
i've expanded it, but now im lost. how do we find k from here?
anonymous
  • anonymous
a_clan, do u know how to solve this using the remainder theorem? :)
A_clan
  • A_clan
f(x)=(3x+k)^3+(4x−7)^2 According to remainder theorem, f(3) = 33 (9+k)^3 + (12 - 7)^2 = 33 Rest is simple calculation.
anonymous
  • anonymous
I got f(x) = 721 + k^3 is it incorrect?
A_clan
  • A_clan
k^3 + 27k^2 + 243k + 721 = 0

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