Given the polynomial function
[tex]P(x)=2 x^{2} -4x+30[/tex]
If (x-3) is a factor of P(x), then
[tex]P(x)=2 x^{2} -4x+30=(x-3)*Q(x)[/tex], for some polynomial Q of 1st degree,
Then according to the factor theorem P(3)=0, because P(3)=(3-3)Q(x)=0*Q(3)=0.
Check
[tex]P(3)=2 (3)^{2} -4(3)+30=18-12+30=36[/tex]≠0
we see that P(3) is not 0, so (x-3) is not a factor of P(x).
Answer: no
