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

1 Answer

=(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)