Find the remainder on dividing the polynomial x⁴ + x³ -3x² + 3x + 1 by the following monomial expression:
x

Question

Find the remainder on dividing the polynomial x4 + x3 -3x2 + 3x + 1 by the following monomial expression:x + π

Philoid · Accepted Answer

We will find remainder using remainder theorem which states that

If a polynomial p(x) is divided by a polynomial x – a then the remainder is p(a)

Let p(x) = x⁴ + x³ - 3x² + 3x + 1

x + π can be written as x – (-π)

comparing x – (-π) with x – a we have here a = -π

⇒ p(a) = p(-π)

⇒ p(-π) = (-π)⁴ + (-π)³ - 3(-π)² + 3(-π) + 1

⇒ p(-π) = π⁴ - π³ - 3π² - 3π + 1

Hence the remainder when p(x) is divided by x + π is π⁴ - π³ - 3π² - 3π + 1

Find the remainder on dividing the polynomial x⁴ + x³ -3x² + 3x + 1 by the following monomial expression:
x + π