Question

Use Factor by Grouping to write g(x) in factored form.

g(x)=x^3+3x^2-25x-75

Please help ASAP I get so confused on this

Answer 1

remember
ab+ac=a(b+c) and
a²-b²=(a-b)(a+b)


group the terms
(x^3+3x^2)+(-25x-75)
factor
(x²)(x+3)+(-25)(x+3)
undistribute the (x+3)
(x+3)(x²-25)
factor that difference of 2 perfect squares
(x+3)(x-5)(x+5)

g(x)=(x+3)(x-5)(x+5)