factor by grouping, Assume any variable exponents represent whole numbers x^3-4x^2+5x-20

Question

anonymous · Answer

Is there a common factor you see in $x^3-4x^2$? What about in $5x-20$?

anonymous · Answer

the x and that 20 can be divided into 5

anonymous · Answer

which ever way that goes

anonymous · Answer

@criddle3583 only one $x$ in common in $x^3-4x^2$?
for the $5$, you're right -- $5x-20=5(x-4)$. We're getting close.

anonymous · Answer

and x+5 so its (x-4)(x+5)

anonymous · Answer

Nope @criddle3583... not quite... :-)

anonymous · Answer

We can actually find that $x^2$ is in common in $x^3-4x^2$, so we can factor it out to yield $x^3-4x^2=x^2(x-4)$. So our entire expression is then just$$x^2(x-4)+5(x-4)$$-- hey, notice we have an $x-4$ in common which we can factor it. Do so:$$(x-4)(x^2+5)$$

anonymous · Answer

ok thank you :)