Question

Factor completely 5c5 + 60c4 + 180c3.

5c3(c + 6)(c - 6)

5c3(c2 + 12c + 36)

5c3(c + 6)2

5(c + 6)2

Answer 1

\(\Large\color{darkgreen}{ 5c^5 + 60c^4 + 180c^3 }\)
\(\Large\color{darkgreen}{ (5c^3)c^2 + (5c^3)12c + (5c^3)36 }\)
\(\Large\color{darkgreen}{ 5c^3(c^2 + 12c +36 ) }\)

Answer 2

Now, you need to factor the \(\Large\color{darkgreen}{ c^2 + 12c +36 }\)

Answer 3

5c3(c + 6)(c - 6)?

Answer 4

no....
HINT: `c²+12c+36` is a perfect square.

Answer 5

wait so its just 5c3(c2 + 12c + 36) ?

Answer 6

No it is not

Answer 7

actually you can still factor the second part

Answer 8

Think what 2 numbers multiplied give you 36
but when you add together give you 12

Answer 9

6 and 6

Answer 10

yes but what are your signs
+ +
- -
+ -
-+

Answer 11

+6 and +6

Answer 12

yes now which is it?
recall c times c gives you c^2
6 times 6 gives you 36
+6+6 gives you the middle term of +12
(c+6)(c+6) gives you c^2+12c+36

Answer 13

5c3(c + 6)2?

Answer 14

yes good job

Answer 15

However, you would not cube the 5c in front of your (c+6)

Answer 16

so 5(c + 6)2?

Answer 17

Oh sorry! my fault I made a mistake, you were right. I apologize

Answer 18

\[5c^3(c+6)^2\] is correct

Answer 19

i apologize

Answer 20

the last term is the number you need so in this case it is 36
you list all of the factors of 36
1 times 36
2 times 18
3 times 12
4 times 9
6 times 6
the sign in front of the last term tells you to add all of the terms
1+36=37
2+18=20
3+12=15
4+9=13
6+6=12
sign also, tells you that your sign choices are - - or + +
-6-6=-12
+6+6=+12
we need a +12 for the middle term
put it all together
(c+6)(c+6)