Question

Find the value of p, if the polynomial p(x)=x4-2x3+3x2<br />-px+3p-7 when divided by (x+1) leaves the remainder 19. Also find the remainder when p(x) isdivided by (x+2).

Answer 1

Sol:
Given polynomial p(x) = x4- 2x3 + 3x2- 9x - 7 + 3b.

When divided by x+1 leaves a remainder 29 i.e.

as per the remainder theorem, p(-1) = 29.

But p(-1) = 1 + 2 + 3 + 9 - 7 + 3b = 29

⇒ 8 + 3b = 29

⇒ 3b = 21

∴ b = 7.