Find the value of a such that `(x-4)` is a factor of `5x^3-7x^2-a x-28`

Explanation

Let the given polynomial be `p(x)`.
According to the factor theorem, if `(x−a)` is a factor of `f(x)`, then `f(a)=0`
Then,
`p(4)=0`
`p(4)=5(4)^3−7(4)^2−a(4)−28=0`
`⇒5(64)−7(16)−4a−28=0`
`⇒320−112−4a−28=0`
`⇒320−140−4a=0`
`⇒180−4a=0`
`⇒4a=180`
`⇒a=180/4`
`=>a=45`
`therefore` if `(x−4)` is a factor of `5x^3−7x^2−ax−28` then the value of `a=45`.