Option 2 : 4

**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**