What is the factored form of 3p3 + 27p2 + 24p?

Question

What is the factored form of 3p^3 + 27p^2 + 24p?

A.3p(p − 1)(p − 8)

B.3p(p + 1)(p + 8)

C.3p(p − 2)(p − 4)

D.3p(p + 2)(p + 4)

 

Answer 1

Makayla, we need to figure out what is common between the three terms.  

 

What is common between 3, 27 and 24?  3, right?  3 x 1 = 3, 3 x 9 = 27, and 3 x 8 = 24

 

Now, remember that p³ = p x p x p.  p² = p x p.  

 

What's common between p³, p² and p?  Just p.  p x p² = p³. p x p = p². p x 1 = p

 

Now, let's combine things.  We decided what's in common is both 3 and p, so what is in common is 3p.  We pull it out and combine the rest.

 

3p(p² + 9p + 8)

 

We can also factor p² + 9p + 8.  

 

We need to find two factors of 8 that add together and make 9.  4 and 2?  Nope, that's 6.  8 and 1? Yep, 8 + 1 = 9.

 

We split 9p into 8p + p.  Now, we have p² + 8p + p + 8.

 

What is in common between the first two terms?  p.  p(p + 8) = p² + 8p

 

What is in common between the second two terms?  Just 1. 1(p + 8) = p + 8

 

We combine the two.  p(p + 8) + 1(p + 8).  Because they both have p + 8, we combine what's in front into their own parentheses.

 

(p + 1)(p + 8)

 

Let's not forget about the 3p that was in front!  3p(p + 1)(p + 8)

 

Hope this helps!