The remainder theorem? helpp, thanks :)

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The remainder theorem? helpp, thanks :)

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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(3x+k)^3 + (4x-7)^2 has a remainder of 33 when divided by x-3. what is k? :)
so substitute x = 3 into the polynomial (3x3 +k)^3 + (4 x 3 - 7)^2 = 33 (9 + k)^3 + (5)^2 = 33 (9 +k)^3 = 8 take cube root of both sides (9 + k) = 2 I'll let you find k
we are given that on division we get remainder of 33 so we have (3x+k)^3+(4x-7)^2=(Ax^+Bx+C)(x-3)+33 A, B and C are constants now put x=3 in the above equation we'll get (9+k)^3+(12-7)^2=0+33 (9+k)^3+25=33 (9+k)^3=8 8=2^3 so (9+k)^3=2^3 or 9+k=2 k=-7

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thanks guys :) but.. why is 8=2^3?
(9+k)^3+(12-7)^2=0+33 (9+k)^3+25=33 (9+k)^3=8 8=2^3 so (9+k)^3=2^3 or 9+k=2 k=-
thanks! :)

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