Question

One of the factors of p5 - 144p3 is

p3

p + 12

p - 12

All of the above

Answer 1

can any whole number be taken out of it? or only variables?

Answer 2

144p3?

Answer 3

if you take a number out of one then you must also take it out of the other. In this case, the p^5 does not have a number in front of it besides 1 so you cannot take out any number from it

Answer 4

so i take out 144?

Answer 5

if you only look now at the p's, do what we did with the a's before so

p * p * p * p * p
p * p * p

Answer 6

no, you cannot take out the 144.

Answer 7

What can you factor out of \(\ p^5 - 144p^3\)? What's their gcf is what I'm trying to say, it doesn't have a coefficient gcf. So you're only left with a variable gcf. What is it?

Hint: When you're doing problems like this you always chose the smallest power because:



They both have in common \(\ p^3 \)

When you factor "p^3" from p^5 - 144p^3

You have p^3 (p^2 - 144), you can still keep going, \(\ (p^2 - 144) \implies \sqrt{(p^2 - 144)} \implies \sqrt{p^2} - \sqrt{144}\)

\(\ \sf \sqrt{p^2} = p \) and \(\ \sf \sqrt{144} = 12 \) ... and becasue it's negative you have 2 parts to it. (p - 12)^2 = (p - 12)(p + 12)

Therefore your factored equation is now:

\(\ \sf p^3(p + 12)(p-12) \)