Answer:
The factored form is (x+2)(2x+5)(2x-5)
Step-by-step explanation:
The given expression which we need to factor is [tex]4x^3+8x^2-25x-50[/tex]
We can factor it by grouping method.
Make groups as shown below.
[tex](4x^3+8x^2)+(-25x-50)[/tex]
Take GCF from each groups
[tex]4x^2(x+2)-25(x+2)[/tex]
Factored out the common terms
[tex](x+2)(4x^2-25)[/tex]
Now, we can further factored [tex]4x^2-25[/tex] using the difference of squares formula [tex]a^2-b^2=(a+b)(a-b)[/tex]
Writing in perfect square form
[tex](x+2)((2x)^2-5^2)[/tex]
Using the difference of square formula
[tex](x+2)(2x+5)(2x-5)[/tex]
Thus, the factored form is (x+2)(2x+5)(2x-5)
