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