Question

if the remainder on division of x3+2x2+Kx+3 by x-3 is 21 find the quotient and the value of k​

Answer 1

Answer:

Step-by-step explanation:

Dividend: f(x) = x3 + 2x2 + kx + 3,

Divisor: g(x) = x - 3 and remainder, r (x) = 21

Using the remainder,we have the following expression:

f(3) = 21

 

The polynomial p(x) is x3 + 2x2 - 9x + 3.

Now, on long division, we get  

 

Thus, x3 + 2x2 - 9x + 3 = (x - 3 ) (x2 + 5x + 6) + 21

∴ The quotient = x2 + 5x + 6

Clearly, x3 + 2x2 - 9x - 18

= (x - 3 ) (x2 + 5x + 6)  

= (x - 3 ) (x + 2)(x + 3)

Therefore, the zeroes of x3 + 2x2 - 9x - 18 are 3, -2 and -3.