f^3+2f^2-64f-128 factor each polynomial

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baxthum8 eNotes educator| Certified Educator

Factor `f^3+2f^2-64f-128`

First, group the polynomial in to 2 sections: `(f^3+2f^2) ` and `(-64f-128)`

Find what's common in each section and factor the commonalities out of the 2 terms:  `f^3 + 2f^2 = f^2(f+2)` and `-64f-128 = -64(f+2)`

If each of the 2 terms contain the same factor, then combine the factors together.

This gives you: `(f+2)(f^2-64)`

Since the 2nd term `f^2-64` represents the difference of 2 squares, also factor this.

`f^2-64 = (f-8)(f+8)`

This makes the final factored expression:


mchandrea | Student

`f^3 + 2f^2 -64f -128`

`(f^3 + 2f^2) (-64f -128)`

`f^2 (f + 2) -64 (f + 2)`

`(f^2 -64)(f + 2)`


  • In factoring this equation, the first step is to group the polynomial into two. And find common factors.
  • in this case, the common factors are f^2 and -64. Simplify the equation in the parenthesis by isolating the greatest common factor in one side.
  • Group the factors together.
  • The factors could still be simplified. 
  • The final answer should always be in its simplest form.
atyourservice | Student


Your first job is to group the terms (this is to make it a little bit easier to factor)

`(f^3+2f^2) (-64f-128 )`

Now look for the greatest common factor between the terms in the parentheses

Greatest common factor as in a number that can be multiplied to get both of those numbers

The greastest common factor of the first set would by f^2 because they both share an f^2 in common

`f^2 (f+2)`

Now find the greatest common factor for -64f and -128, the biggest number they share is -64

`-64 (f+2)`

now you have `f^2 (f+2)-64 (f+2)`

put the numbers together

`(f^2-64) (f+2)`

set it equal to 0

`f^2-64 = 0`

x= +8, -8



and the answer is f=2 , 8 , -8