Is 2x+5 a factor of x^3+2x^2+5x-5? Explain why or why not.

Question

jim_thompson5910 · Answer

If 2x+5 was a factor, then x = -5/2 would be a root

This is because 2x+5 = 0 turns into x = -5/2 when you solve for x

jim_thompson5910 · Answer

So all you need to do is plug in x = -5/2 and evaluate. If you get 0 as a final result, then 2x+5 is a factor

anonymous · Answer

got it, i didnt know you could just make 2x+5=0 and then solve, the 2x was a little confusing. thanks.

jim_thompson5910 · Answer

yw

the reason why you can do it is say q(x) times 2x+5 would give you x^3+2x^2+5x-5

in other words

x^3+2x^2+5x-5 = (2x+5)(q(x))

So if x^3+2x^2+5x-5 = 0, then 


(2x+5)(q(x)) = 0

2x+5 = 0 or  q(x) = 0

etc etc

anonymous · Answer

ah got it

agent0smith · Answer

You can also check it by synthetic division, if you've done that.

anonymous · Answer

my final answers was -20.625, after plugging in -5/2

jim_thompson5910 · Answer

so that means that 2x+5 isn't a factor

anonymous · Answer

yeah