Answer:
Final factor is [tex](x + 3)(x+5)(x-5)[/tex].
Step-by-step explanation:
Given expression is [tex]x^3 + 3x^2 - 25x -75[/tex]
Now we need to factor that expression [tex]x^3 + 3x^2 - 25x -75[/tex] by grouping. So let's make group of first two terms and group of last two terms.
[tex]x^3 + 3x^2 - 25x -75[/tex]
[tex]=(x^3 + 3x^2)+( - 25x -75)[/tex]
factor each group
[tex]=x^2(x + 3)-25(x +3)[/tex]
[tex]=(x + 3)(x^2-25)[/tex]
[tex]=(x + 3)(x+5)(x-5)[/tex]
Hence final factor is [tex](x + 3)(x+5)(x-5)[/tex].
