If f(x) = x⁴ – 2x² + ax – b is divided by (x – 2), the remainder is 4. If (a + b) = –4. Find the value of a.

Concept Used:

Remainder theorem: If a polynomial f(x) is divided by (x – a) then f(a) will give the remainder.

Explanation:

f(x) = x⁴ – 2x² + ax – b

f(2) = (2)⁴ – 2(2)² + a.2 + b

f(2) = 16 – 8 + 2a + b

f(2) = 8 + 2a + b

f(2) = 4

8 + 2a + b = 4

2a + b = –4

a + (a + b) = –4

a – 4 = –4

a = 0

Hence, the value of a is 0.