Question

How do you factor `x^3 + 3x^2 + 7x + 21`?

Answer 1

`f(x) = x^3 + 3x^2 + 7x + 21 = 0.`

Try small numbers: 1, 2, 3, -3...

f(-3) = - 27 + 27 - 21 + 21 = 0, then (x + 3) is a factor.

`f(x) = (x + 3)(x^2 + 7)`

Check: Develop `f(x) = x^3 + 7x + 3x^2 + 21.`Correct