Question

Factor completely 4x3 + 8x2 − 25x − 50.

Answer 1

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)

Answer 2

$4x^3 + 8x^2 - 25x - 50 = \\ 4x^2(x + 2) - 25(x + 2)=\\ (4x^2 - 25)(x+2)=\\\\ \boxed{\bf{(2x - 5)(2x + 5)(x+2)}}$