Question

Factor completely (linear factors only): `f(x)=3x^4+10x^3+24x^2+22x+5`?

Answer 1

=`(x+1)(3x+1)(x+1+2i)(x+1-2i)`

Explanation:

`3x^4+10x^3+24x^2+22x+5`

=`3x^4+3x^3+7x^3+7x^2+17x^2+17x+5x+5`

=`3x^3*(x+1)+7x^2*(x+1)+17x*(x+1)+5*(x+1)`

=`(x+1)*(3x^3+7x^2+17x+5)`

=`(x+1)*(3x^3+x^2+6x^2+2x+15x+5)`

=`(x+1)*[x^2(3x+1)+2x(3x+1)+5(3x+1)]`

=`(x+1)(3x+1)(x^2+2x+5)`

=`(x+1)(3x+1)[x^2+2x+1-(-4)]`

=`(x+1)(3x+1)[(x+1)^2-(2i)^2]`

=`(x+1)(3x+1)(x+1+2i)(x+1-2i)`