How do you use synthetic division to show that x=1/2 is a zero of #2x^3-15x^2+27x-10=0#?

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Answer 1 · 2018-07-12T16:11:35

Please see the explanation below

Divide by #1/2#

#color(white)(aaaa)##1/2##|##color(white)(aaaa)##2##color(white)(aaaa)##-15##color(white)(aaaaaa)##27##color(white)(aaaaaa)##-10#

#color(white)(aaaaaa)##|##color(white)(aaaa)##color(white)(aaaaaaa)##1##color(white)(aaaaa)##-7##color(white)(aaaaaaaa)##10#

#color(white)(aaaaaaaaa)###_________________________________________________________##

#color(white)(aaaaaa)##|##color(white)(aaaa)##2##color(white)(aaaa)##-14##color(white)(aaaaaa)##20##color(white)(aaaaaaaa)##color(red)(0)#

The remainder is #=(0)# and the quotient is #=(2x^2-14x+20)#

As the remainder #=0#, #x=1/2# is a root of #2x^3-15x^2+27x-10#

#2x^3-15x^2+27x-10=(2x^2-14x+20)(x-1/2)#