Question

find the value of k if x-3 is the factor of kx^²x^³-kx^²+3kx-k​

Answer 1

Let f(x) be the given polynomial.

f(x)=k²x³-kx²+3kx-k

Given that x=3

If (x - @) is a factor of a polynomial,then @ is zero of a polynomial

So,

f(x)=f(3)

Substituting the required value,

f(3)=k²x³-kx²+3kx-k

→0 = k²(3)³-k(3)²+3k(3)-k

→0=27k²-9k+9k-k

→27k²-k=0

→k(27k-1)=0

→k=0 or 27k=1

→k=1/27 or 0