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Given the polynomial function
If (x-3) is a factor of P(x), then
, 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
≠0
we see that P(3) is not 0, so (x-3) is not a factor of P(x).
Answer: no
If (x-3) is a factor of P(x), then
Then according to the factor theorem P(3)=0, because P(3)=(3-3)Q(x)=0*Q(3)=0.
Check
we see that P(3) is not 0, so (x-3) is not a factor of P(x).
Answer: no