How to factor x3−8x2+15x?

1 Answer
Don't Memorise
Apr 9, 2015

We can see that x is common to all the terms. We can write it as

x⋅(x2−8x+15)

Now we need to factorise x2−8x+15

We can use Splitting the Middle Term technique to factorise this.

It is in the form ax2+bx+c where a=1,b=−8,c=15

To split the middle term, we need to think of two numbers N1andN2 such that:
N1⋅N2=a⋅candN1+N2=b
N1⋅N2=(1)⋅(15)andN1+N2=−8
N1⋅N2=15andN1+N2=−8

After Trial and Error, we get N1=−3andN2=−5
(−3)⋅(−5)=15 and (−3)+(−5)=−8

So we can write the expression x2−8x+15 as
x2−3x−5x+15
=x(x−3)−5(x−3)
=(x−3)⋅(x−5)

x3−8x2+15x=x⋅(x−3)⋅(x−5)

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