For what value of `a` is `(x-5)` a factor of `x^3-3x^2+a x-10` ?

Explanation

Let `p(x)=x^3−3x^2+ax−10` and it is given that `(x−5)` is a factor of `p(x)`,
By factor theorem
`p(5)=0`
`=>p(5)=5^3−(3×5^2)+(a×5)−10`
`=125−(3×25)+5a−10`
`=125−75+5a−10=5a+125−8`
`=5a+40`
Now equate `p(5)=0`:
`=>5a+40=0`
`⇒5a=−40`
`⇒a=−40/5`
`⇒a=−8`
`therefore a=−8.`