Question

If the polynomial t³ - 3t² + kt + 50 is divided by (t -3), the remainder is 62. Find the value of k.​

Answer 1

$\huge\underline\frak{\fbox{AnSwEr :-}}$

When given polynomial is divided by (t -3) the remainder is 62. It means the value of the polynomial when t= 3 is 62.

$\leadsto$ P(t)= t³ - 3t² + kt + 50

By remainder theorem,

$\leadsto$ Remainder = p(3) = 3³ - 3 x 3² + k x 3 + 50

$\leadsto$ 27 - 3 x 9+ 3k + 50

$\leadsto$ 27 - 27+ 3k + 50

$\leadsto$ 3k + 50

$\leadsto$ 3k + 50 = 62

$\leadsto$ 3k - 62 - 50

$\leadsto$ 3k = 12

$\leadsto$ k = $\large\sf\frac{12}{3}$

$\implies$ k = 4

But remainder is 62 and k = 4