Concept:Use the relationship: P(x)=q(x)×d(x)+r(x) to find the polynomial.Explanation:Substitute q(x)=x2−x−5, d(x)=3x−1 and r(x)=7.So, P(x)=(x2−x−5)(3x−1)+7.Expand the brackets: (x2−x−5)(3x−1)=3x3−x2−3x2+x−15x+5.Combine like terms: 3x3−4x2−14x+5.Now add the remainder 7: P(x)=3x3−4x2−14x+5+7.Simplify: P(x)=3x3−4x2−14x+12.Answer:3x3−4x2−14x+12 (Option A).