Question

find the value of k if x -3 is a factor of
${k}^{2} {x}^{3} \: - k {x}^{2} + \: 3kx - \: k$
class - 9
polynomials

Answer 1

Hey!!!!

Good Morning

_________________

Let p(x) = k²x³ - kx² + 3kx - k

Given x - 3 is a factor of k²x³ - kx² + 3kx - k

Then x - 3 = 0

=> x = 3 is a zero of the p(x)

Then p(3) = 0

=> k²(3)³ - k(3)² + 3k(3) - k = 0

=> 27k² - 9k + 9k - k = 0

=> 27k² - k = 0

=> k(27k - 1) = 0

Case 1, k = 0 <<<<< Answer

Case 2, 27k - 1 = 0

=> k = 1/27 <<<<<< Answer

______________

Hope this helps ✌️