Question

I need to completely factor an equation but this is as far as I got (x+2)(x3−x2−6x+18) is that correct? Or can I still factor that?

Answer 1

@SolomonZelman

Answer 2

https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-by-grouping/v/factor-by-grouping-and-factoring-completely

Answer 3

@january123 I understand that but mine is (x+2)(x^3−x^2−6x+18) instead of X^2.....and so on mine starts with 3rd power

Answer 4

Oh okay...I don't really know that much about math...tag other ppl

Answer 5

ok thank you for trying to help :)

Answer 6

@mathmate can you help me?

Answer 7

yw and sorry!

Answer 8

is ok :)

Answer 9

What are you trying to factorize?
is it
x^4+x^3-8*x^2+6*x+36

Answer 10

yes lol wow you found it xD but I already got up to here (x+2)(x^3−x^2−6x+18) and I need to completely factor

Answer 11

Yes, the cubic can be factored further.

Answer 12

but how can you show me?

Answer 13

You are familiar with the factor theorem?
If not, you can read this:
http://www.purplemath.com/modules/factrthm.htm

Answer 14

yes a=0 right?

Answer 15

I don't quite catch what you mean by a=0! :(

Answer 16

no nvm I got it but aren't you supposed to use the factor theorem when you have something that you are able to factor by? or do I have to use synthetic formula by factoring the second parenthesis by the second?

Answer 17

by the first I mean sorry

Answer 18

In any case, the factor theorem basically means that if (x-k) is a factor to a polynomial p(x), then p(k)=0.
In other words, if we substitute a value for x that can make the polynomial zero, we found the factor.
Is that ok so far?

Answer 19

yeah and I got -2 for that

Answer 20

What I will show you will not require synthetic division to find the factor, but you need to do synthetic division AFTER you've found the factor (like what you did before) to find the remaining factors, if any.

Answer 21

You also know that (by the factor theorem), if (x-k) is a factor, then k is a factor of the constant term.
Here the constant term is 18, so the integer factors are:

Answer 22

Can you give me the integer factors of 18?

Answer 23

wasn't it 36?
and yeah positive and negative 1,2,3,6,9,18

Answer 24

Excellent!

Answer 25

ohhh I think Im getting what you mean :D

Answer 26

To proceed systematically, we will make a table.

Answer 27

to pretty much keep repeating what I did to get the first result :)

Answer 28

We will tabulate the values of each term.
But we don't know the sign of the factor, so we will be contented with just tabulating the absolute value of each term.

Answer 29

Like this:

Answer 30

Value x^3 x^2 6x 18
1 1 1 6 18
2 8 4 6 18
3 27 9 18 18
6 216 36 36 18
9 729 81 54 18
18...

Answer 31

Now go through each line to see if you can find a way to add or subtract numbers to make zero.
for k=1,
1 1 6 18
we will never make the sum to zero, no matter which + or - sign we give the numbers.
So far so good?

Answer 32

So x+1 or x-1 cannot be a factor.

Answer 33

Can you try for x=2, where the terms are 8, 4, 6, 18,
and see if you can add or subtract the numbers to make zero?

Answer 34

hold on my computer is freezing brbr