Question

Factor the following four-term polynomial by grouping. x^3+5x^2+x+5

Answer 1

See what you can factor from first two terms, then see what you can factor from last two terms.

Answer 2

What common factor is there in x^3 + 5x^2?

Answer 3

\[k \ge 5;0\]

Answer 4

x^3?

Answer 5

No, because there is no x^3 in the second term. It's only x^2.
Now factor that x^2 from first two terms:
x^3 + 5x^2 + x + 5 =
x^2(x + 5) + x + 5
Now since there is nothing that can be factored out of the last two terms, x + 5, you can always say you can factor 1, so do ti:
x^2(x + 5) + 1(x + 5)
Now you have the same factor of x + 5 in the first part and in the second part, so factor out x + 5:
(x + 5)(x^2 + 1)