Question

PLEASE,PLEASE,PLEASE HELP ME!?

Explain, in complete sentences, how you would factor 24x3+ 72x2+ 30x

Answer 1

look for the same letter or number in each term
remember that x^3 (not x3 which could mean 3*x) is x*x*x
so you should see every term has at least one x

Answer 2

24x3+ 72x2+ 30x = 6x(4x^2 + 9x + 5) = 6x( 4x^2 + 4x + 5x + 5) = 6x(4x(x + 1) + 5(x+ 1) )= 6x(4x + 5) (x + 1).

Answer 3

6x(2x+5)(2x+1)

Answer 4

the numbers are actually harder
you can see each number is even so can be written as 2*another number
so 2 is in each term.

the way to find all the common numbers is factor the numbers into their prime factors
24 is 2*12 = 2*2*6= 2*2*2*3
72= 2*36= 2*2*18= 2*2*2*9= 2*2*2*3*3
30= 2*15= 2*3*5


it look like each number has a 2*3
so factor out a 6

Answer 5

6x(4x + 5) ( x + 1) is the answer

Answer 6

once you figure out 6x is in each term, you write
24x3+ 72x2+ 30x
as 6x* 4x^2 + 6x* 12x + 6x*5 or "undistributing" factoring out 6x
6x(4x^2 +12x +5)

Answer 7

now you can try to factor the quadratic, which is harder

Answer 8

4x^2 +12x +5

first, write down the different ways to factor 5 (the last number)
1*5 =5 (thank goodness only 1 way)
do the same for the 1st number 4
1*4=4
2*2=4

now we take combinations of the 1 and 5 with 1 and 4
we get 1*1 + 4*5 or 1*5 + 4*1
can we get a 12 ? no
now try 1 and 5 and 2 and 2
2*1 +2*5 =12 so those are the numbers

(this is ugly)
(2x +1)(2x+5) should be the factors

Answer 9

It's easier if the number in front of the x^2 is 1 (and not 4)

Answer 10

thank youuu!!!! so much!