If the polynomial t3 – 3t2 + kt + 50 is divided by (t – 3 ) the
remainder is 62. Find the value of k.
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When given polynomial is divided by (t – 3) the remainder is 62. It means the value of the polynomial when t = 3 is 62. p(t) = t3 – 3t2 + kt + 50 By remainder theorem, Remainder = p(3) = 33 – 32 + k x 3 + 50
= 27 – 3 x 9 + 3k + 50
= 27 – 27 + 3k + 50
= 3k + 50
But remainder is 62.
∴ 3k + 50 = 62
∴ 3k = 62 – 50
∴ 3k = 12
∴ k = 4
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