Concept: Remainder Theorem: Let p(x) be any polynomial of degree greater than or equal to one and 'a' be any real number. If p(x) is divided by (x - a), then the remainder is equal to p(a). If two polynomials p(x) and q(x) when divided by (x - a) leave the same remainder, we get ∴ p(a) = q(a) Calculation: We have p(x) = bx3 - 5x2 - 5x + 10 and q(x) = x4 - 3x2 + b Then, the remainders when p(x) and q(x) are divided by (x - 3) are p(3) and q(3) respectively. Since both polynomials leave the same remainders when divided by (x - 3), ⇒ p(3) = q(3) ⇒ b(3)3 - 5(3)2 - 5(3) + 10 = (3)4 - 3(3)2 + b ⇒ 27b - 45 - 15 + 10 = 81 - 27 + b ⇒ 26b - 50 = 54 ⇒ 26b = 104 ⇒ b = 104/26 ⇒ b = 4