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

-r⁵ + 3r⁴ + 18r³

 

can be broken down into these factors (a factor is a number you can multiply together to get another number):

  (-1)*r*r*r*r*r  +  3*r*r*r*r  +  2*3*3*r*r*r

Each term in the expression is now broken down into its factors.  Are there any factors that are common?

 

Well, yes, each of the three terms in the expression has r*r*r in it, so let's factor it out (that is, make r*r*r one of the factors of a new expression:

    r*r*r*( (-1)*r*r + 3*r + 2*3*3 )

 

Now, one of the factors in that expression [the one that is (-r²+3r+18)] is the product of some other factors.  What are they?

 

   r*r*r*(-1)( r*r - 3*r + 2*3*3 )           or      r³(-1)(r²-3r-18)   

   r*r*r*(-1)( r+3 )( r-6 )                  or    r³(-1)(r+3)(r-6)

 

Can any of these terms be further broken down into factors?  No.

 

So, what we did was (1) find the GCF, then (2) factor the polynomial.

 

Did you get all those very specific terms????