Given polynomial = p(x) = x4 – 2x3 + 3x2 – ax + 3a – 7
When p(x) is divided by (x + 1) leaves the remainder is 19.
∴ p(-1) = 19
p(-1) = (-1)4 – 2(-1)3 + 3(-1)2 – a(-1) + 3a – 7 = 19
⇒ 1 + 2 + 3 + a + 3a – 7 = 19
⇒ 4a – 1 = 19
⇒ 4a = 20
⇒ a = 20 ÷ 4 = 5
p(x) = x4 – 2x3 + 3x2 – 5x + 8
p(x) is divided by (x + 2), then p(-2).
P(-2) = (-2)4 – 2(-2)3 + 3(-2)2 – 5(-2) + 8
= 16 + 16 + 12 + 10 + 8 = 62
Required remainder = 62.