Question

Simplify into a binomial

Answer 1

Answer:

$x-5$

Step-by-step explanation:

Consider the expression

$\dfrac{3x^3-15x^2+15x-75}{3x^2+15}$

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

$\dfrac{(x-5)(3x^2+15)}{3x^2+15}=x-5$

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