Write the remainder when the polynomial f(x) =x³+x²-3x+2 is divided by x+1.

is divided by (x-a)

In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x):

f(x) = 4x³-12x²+14x-3, g(x) = 2x-1

In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x):

f(x) = 2x⁴-6x³+2x²-x+2, g(x) = x+2

When (x³¹ + 31) is divided by (x + 1), the remainder is

is divided by (3x+2)

Find the remainder when p (x) = 4x³ + 8x² – 17x + 10 is divided by (2x – 1).

Show that:

(i) 𝑥 + 3 is a factor of 69 + 11𝑥−𝑥² + 𝑥³.

(ii) 2𝑥−3 is a factor of 𝑥 + 2𝑥³ – 9𝑥² + 12

When p (x) = (x³ + ax² + 2x + a) is divided by (x + a), the remainder is

If p (x) = 2x³ + ax² + 3x – 5 and q (x) = x³ + x² – 4x + a leave the same remainder when divided by (x – 2), show that

If (x³ + mx² – x + 6) has (x - 2) as a factor and leaves a remainder r, when divided by (x - 3), find the values of m and r.