Question

Simplify into a binomial

Answer 1

`x-5`

Explanation:

Consider the expression

`(3x^3-15x^2+15x-75)/(3x^2+15)`

Its numerator
`3x^3-15x^2+15x-75` is equivalent to

`3x^3-15x^2+15x-75\\ \\=3x^2(x-5)+15(x-5)\\ \\=(x-5)(3x^2+15)`

Therefore, given expression can be rewritten as

`((x-5)(3x^2+15))/(3x^2+15)=x-5`

Note that
`3x^2+15\\eq 0,` so we can divide the numerator and the denominator by non-zero expression
`3x^2+15.`