Given that (x - 5) is a factor of
[tex]f(x)=x^3+2x^2+cx+10[/tex]
Since x - 5 is a factor,
[tex]\begin{gathered} x-5=0 \\ x=5 \end{gathered}[/tex]
x = 5 is one of the roots of the equation,
Substitute 5 for x into the eqaution to find c
[tex]\begin{gathered} f(x)=x^3+2x^2+cx+10 \\ f(5)=5^3^{}+2(5)^2+c(5)+10=0 \\ 5^3+2(5)^2+c(5)+10=0 \\ 125+2(25)+5c+10=0 \\ 125+50+5c+10=0 \\ \text{Collect like terms} \\ 125+50+10+5c=0 \\ 185+5c=0 \\ 5c=-185 \\ \text{Divide both sides by 5} \\ \frac{5c}{5}=-\frac{185}{5} \\ c=-37 \end{gathered}[/tex]
Hence, the value of c for which (x - 5) is a factor is -37
