Question

Fund the value of k for which x-k is the factor of the polynomial f (x)= x^5-k^2x^3+ 2x+k-3.
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Answer 1

Answer:

Step-by-step explanation:

by remainder theorem

we get

x-k=0

x=k

if k is a factor of F(x) then the value of f(k) becomes 0

{by factor theorem}

$f (x)= x^5-k^2x^3+ 2x+k-3.$

$f (k)= k^5-k^2k^3+ 2k+k-3.$

$f(k)=k^5-k^5+2k+k-3$

$f(k)=3k-3$

3k-3=0

{because x-k is a facor of given expression}

k=3/3

k=1