Need help with factoring. 5x^.5+x+4

Question

akashdeepdeb · Answer

$$5\sqrt{x} + x + 4$$ 
$$Take ~~\sqrt{x} = y~~~\therefore ~~x = y^2$$
We do this so that we can get rid of the radical and we can factor it easily and then substitute $\sqrt{x}$ back in the factored polynomial. 

Our polynomial now becomes: $5y + y^2 + 4 = y^2 + 5y + 4$

Can you factorize this now? :)

anonymous · Answer

(y+4)(y+1)? But I still dont see how this gives me the factor of the inital equation.

anonymous · Answer

Unless I replace the y with square root of x?

anonymous · Answer

I don't know.

jhannybean · Answer

we can rewrite this as $\ x+5\sqrt{x} +4$  so all we have to think about is what multiplies to give us 4 and adds to give us 5?

anonymous · Answer

4 and 1?

jhannybean · Answer

Yep, and you know that $\ x = \sqrt{x} \cdot \sqrt{x} $

jhannybean · Answer

Therefore you can factor it out as : $\ (\sqrt{x} +1)(\sqrt{x}+4)$

anonymous · Answer

Oh, I  get it now. And I see where Aka was going with this earlier.

freckles · Answer

You are exactly right to replace that y up there with sqrt(x)

anonymous · Answer

Thanks for all your help :)

jhannybean · Answer

Yeah, me and him had 2 different approaches :P