Polynomial p(x) has integer coefficients and p(3)=−2.
For what values n may it be possible for (x-n) to be a factor of p(x)?
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16 choices
1. If (x-n) is a factor of p(x) then
p(x)=(x-n)*q(x) with q(x) another polynomial with integer coefficients.
2. If p(3)=-2 then the last term of the polynomial p(x) is 2 (mod 3), and, it follows that, no multiple of 3 could be a factor of p(x)
3. If p(3)=2 and (x-n) is a factor of p(x), then:
(3-n)*(q(3))=-2
But as (3-n) and q(3) are integers this only leaves room for:
[(3-n),q(3)]= [(2,-1), (1,-2), (-1, 2), (-2, 1)]
Then n is compatible only with the values:
n=(5, 4, 2, 1)
Edited on February 10, 2019, 3:33 am
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Posted by armando
on 2019-02-10 03:30:51 |
Solution