Answer:
[tex]\boxed{\textsf {The value of c is $\sf \dfrac{-14}{3}$. }}[/tex]
Step-by-step explanation:
A polynomial is given to us . We need to find the value of c so that it is divisible by (x-3 ) .The given polynomial to us is ,
[tex]\sf \implies p(x)=- x^3+cx^2-4x+3 [/tex]
And the factor is ,
[tex]\sf \implies g(x) = x + 3 [/tex]
Now , according to factor theorem , p(x) will be divisible by g(x) if p(-3) = 0
[tex]\sf \implies p(x)= - x^3+cx^2-4x+3 \\\\\implies\sf p(-3) = 0 \\\\\sf\implies -(-3)^3+c(-3)^2-4(-3)+3 = 0 \\\\\sf\implies 27 + 9c +12+3=0 \\\\\sf\implies 9c +42=0 \\\\\sf\implies 9c = (-42) \\\\\sf\implies c = \dfrac{-42}{9}\\\\\sf\implies \boxed{\pink{\sf c = \dfrac{-14}{3}}}[/tex]
