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:
`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.
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
Now find the greatest common factor for -64f and -128, the biggest number they share is -64
now you have `f^2 (f+2)-64 (f+2)`
put the numbers together
set it equal to 0
`f^2-64 = 0`
x= +8, -8
and the answer is f=2 , 8 , -8