**Given polynomial = p(x) = x**^{4} – 2x^{3} + 3x^{2} – 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) = x^{4} – 2x^{3} + 3x^{2} – 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.**