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

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Answer 1 · 2017-10-05T16:16:45

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

#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)#