When x3+2x2 + kx +3 is divided by ( x-3) then the remainder is 21

1.	When x3+2x2 + kx +3 is divided by ( x-3) then the remainder is 21
Answer» Let p(x) ={tex} x^3 + 2x^2 + kx + 3{/tex}Now, x - 3 = 0\xa0{tex}\\Rightarrow{/tex}\xa0x = 3By the remainder theorem, we know that when p(x) is divided by (x - 3), the remainder is p(3).Now, p(3) = (3)3\xa0+ 2(3)2\xa0+ k(3) + 3= 27 + 2(9) + 3k + 3= 30 + 18 + 3k\xa0= 48 + 3kBut, remainder = 21\xa0{tex}\\Rightarrow{/tex}\xa048 + 3k = 21{tex}\\Rightarrow{/tex} 3k = 21 - 48{tex}\\Rightarrow{/tex}\xa03k = -27{tex}\\Rightarrow{/tex} k = {tex}\\frac{-27}3{/tex}{tex}\\Rightarrow{/tex} k = -9So, the value of k is -9.

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