SOLUTION: Here is the problem I don't understand. Factor this trinomial -45p2

SOLUTION: Here is the problem I don't understand. Factor this trinomial -45p2 - 12p + 12p3

Question 243710: Here is the problem I don't understand.
Factor this trinomial
-45p2 - 12p + 12p3
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression.

Rearrange the terms in descending degree.

Factor out the GCF .

Now let's try to factor the inner expression

---------------------------------------------------------------

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,4,8,16
-1,-2,-4,-8,-16

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*(-16) = -16
2*(-8) = -16
4*(-4) = -16
(-1)*(16) = -16
(-2)*(8) = -16
(-4)*(4) = -16

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First Number	Second Number	Sum
1	-16	1+(-16)=-15
2	-8	2+(-8)=-6
4	-4	4+(-4)=0
-1	16	-1+16=15
-2	8	-2+8=6
-4	4	-4+4=0

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

--------------------------------------------------

So then factors further to

===============================================================

Answer:

So completely factors to .

In other words, .

Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).

RELATED QUESTIONS
Factor this 3p5 �... (answered by nerdybill,Gogonati)

factor trinomial completely. Here is the problem.... (answered by jim_thompson5910)

Factor the following trinomial. {{{9x^2+24x+16}}} I dont understand the steps to... (answered by jim_thompson5910)

Don't understand how the answer to this problem is 15. csc(arctan(square root... (answered by Alan3354,math_tutor2020,MathTherapy)

how do I factor by grouping. here is my problem and I don't know how to do it without a... (answered by stanbon)

Here's another problem I don't understand. Factor this trinomial 12y2 + 7y - 12 (answered by scott8148)

please help. factor the trinomial -p^2=12p+27 having trouble when there is a... (answered by Earlsdon,venugopalramana)

what is the answer here nP2 = 380 * 10P5 = ? * 8Pr = 20160 * 6P6 = ? * 7Pr... (answered by MathLover1,greenestamps,MathTherapy)

How is this algebra problem done? factor... (answered by jim_thompson5910)