Question

Factor completely!
x^3+2x^2+x+2

Answer 1

groups the 1st two, see what you get for a common factor

Answer 2

thats the thing, idk what the GCF is :(

Answer 3

hmm, well, ok, let's try this one

ab, ca, da <--- what's a COMMON factor in those 3 pairs?

Answer 4

a?

Answer 5

yup.

Answer 6

right

Answer 7

So look at the first two terms, and see if once you factor out the common factor you have the same thing as the last two terms.

Answer 8

so, group the 1st two there with a parentheses, and see "what is common" to get the GCF

Answer 9

well grouping n pairs works

\[(x^3 + x)+(2x^2 + 2)\]

now find some common factors...in each pair

Answer 10

is it x^2 for the first two terms?

Answer 11

yes, btw @campbell_st grouping will work the same, but yes, is \(x^2\), so take that out of the parentheses

Answer 12

THANK YOU GUYS I GOT IT:)

Answer 13

if you are using

\[(x^3 + 2x^2) + (x + 2)\]

you're correct

and there are several groupings that will result in the same answer

Answer 14

yea thanks for helping!

Answer 15

The terms with even powers vs odd powers of x, for example, would also work.

Answer 16

so after you group them , what do you do next?

Answer 17

Factor out the common factor (see @campbell_st 's response) and see what's left.

Answer 18

$$
\pmatrix{x^2\color{blue}{(x+2)}+\color{blue}{(x+2)}}\\
\text{see anything common on those 2 binomials}
$$

Answer 19

@jdoe0001 - exactly.

Answer 20

yup so it would be (\[(x^{2})(x+2)(x+2)\]

Answer 21

or no?

Answer 22

well, lemme rewrite that differently

Answer 23

No, it's (x^2+1)(x+2) because the (x^2)(x+2)+(x+2) can have the (x+2) factored out, which leaves x^2+1.

Answer 24

$$
(x+2)=\color{blue}{a}\\
\pmatrix{x^2\color{blue}{a}+\color{blue}{a}}\\
\text{see anything common on those 2 binomials?}
$$

Answer 25

guys isn't the answer (x+2)(x+i)(x-i)??

Answer 26

yes :)

Answer 27

If you're willing to get into imaginary numbers. Sometimes you want to keep it real.

Answer 28

well, I guess he meant x-1 :)

Answer 29

ohh.... wait... haemm one sec

Answer 30

$$
\pmatrix{x^2\color{blue}{(x+2)}+\color{blue}{(x+2)}} \implies (x+2)(x^2+1)\\
$$

Answer 31

I gather you can expand the squared one further by making it \(\large x^-(-1)^2\) but not sure it's necessary :|

Answer 32

yea my teacher said it was that, i wasn't sure so i asked

Answer 33

ok

Answer 34

hmm, nevermind the above heehe, \((-1)^2\) is ... null for this specific :)

Answer 35

It's actually \[(x)^2-(\sqrt {-1})^2\]