The polynomial remainder theorem states that if a polynomial p(x) is divided by (x - a), the remainder is p(a).
We need to determine which of the polynomials give -7 as the remainder when divided by x - 2. We only need to substitute x by 2.
A.
[tex]3(2)^3+6(2)-2=24+12-2=34[/tex]
B.
[tex]2^3-2(2)^2-4(2)+1=8-8-8+1=-7[/tex]
This is the correct answer: B.
