How do you find the factors of #f(z)# over C if #f(z)=2z^3+3z^2-14z-15#?

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Answer 1 · 2016-09-17T19:14:22

#(z+1)(z+3)(2z-5)#.

We observe that,

The Sum of the co-effs. of odd powered terms of #z# is

#2-14=-12#,

and, that of even powered, #3-15=-12#

We conclude that #(z+1)# is a factor of #f(z)#.

#"Now, "f(z)=2z^3+3z^2-14z-15#

#=ul(2z^3+2z^2)+ul(z^2+z)-ul(15z-15)#

#=2z^2(z+1)+z(z+1)-15(z+1)#

#=(z+1)(2z^2+z-15)#

#=(z+1){ul(2z^2+6z)-ul(5z-15)}#

#=(z+1){2z(z+3)-5(z+3)}#

#=(z+1)(z+3)(2z-5)#.