could someone help me understand this?

Question

Factor the following problem completely. First factor out the greatest common factor, and then factor the remaining trinomial.

 

r⁵+3r⁴ +18r³

Answer 1

The greatest common factor is r³  so

 

 r⁵ + 3 r⁴ +18 r³  =   r³ ( r² +3 r + 18)

 

 The trinomial r² + 3 r +18 does not factor with real numbers.  
The problem was probably supposed have -18 instead of +18

In that case the trinomial would be  r² + 3r -18 which does factor as

 

    r² + 3 r  -18 =  (r -3) (r + 6)

 

The full answer would then be   r³ ( r -3) (r + 6)