Answer:
x = square root of 2
x = -5
Explanation:
The main thing to do in all of these problems is to solve for x. In order to do that with four terms, you need to use a different method of factoring: factor by grouping.
Example 1:
f(x) = x^3 + 5x^2 - 2x - 10
We take the first two terms and figure out what we can factor out by seeing what what they have in common. Both terms have a x^2 or greater so take that out.
f(x) = [ x^2 (x + 5) ] + [ -2x - 10 ]
For the third and fourth terms, we see that they have a 2 in common because you can multiply both numbers by 2. HOWEVER, because you have a x + 5 as a multiple in the other factor, you need to make them match up, so you take out a -2 instead of a 2.
f(x) = [ x^2 (x + 5) ] + [ -2 (x + 5) ]
Then you put the terms you factored out into a parenthesis and the ones in parenthesis as another part of the equation.
f(x) = (x^2 - 2) + ( x + 5 )
0 = (x^2 - 2) + ( x + 5 )
0 = (x^2 - 2)
2 = x^2
square root of 2 = x
0 = ( x + 5 )
-5 = x