Question

One of the factors of the polynomial x3 + 5x2 + 6x is (x2 + 3x). What is the other factor?

Answer 1

The given polynomial is :

$x^{3}+5x^{2}+6x$

One factor is given as : $x^{2} +3x$ or $x(x+3)$

So, now solving this for 2nd factor, we get,            

$x(x^{2}+5x+6 )$          

$x[(x^{2}+3x+2x+6)]$          

$x(x+3)(x+2)$              

Hence, the second factor is (x+2)

Answer 2

The answer is 

x (x² + 5x + 6) 
-------------------- 
x ( x + 3) 

( x + 3 ) (x + 2) 
--------------------- 
x + 3 

x + 2