Question

Factor the following four-term polynomial by grouping. x^3+3x^2+x+3

Answer 1

\[x^2(x+3)+(x+3)\] is the first step

Answer 2

second step is \((x^2+1)(x+3)\)

Answer 3

don't understand..

Answer 4

ok did you understand the first step of taking the \(x^2\) and factoring it out of the first two terms?

Answer 5

Yes got that

Answer 6

ok so we have two terms, the first one is \(x^2(x+3)\) and the second one is \(x+3\)

Answer 7

we can visualize it as
\[x^2(x+3)+1(x+3)\]

Answer 8

now there are two terms, and both have a common factor of \(x+3\)
the first time is \(x+3\) times \(x^2\) and the second term is \(x+3\) times \(1\)

Answer 9

so we can factor out the \(x+3\) from both terms and see that you have
\[(x+3)(x^2+1)\]

Answer 10

it's so confusing but so far little by little i got it thank you @satellite73

Answer 11

i'm getting it*