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Showing 1 question for Class 9. Tap a card to reveal the answer.

MathematicsPolynomialsmedium

Using the remainder theorem, find the remainder when p(x) = x^3 + 3x^2 + 3x + 1 is divided by (x + 1).

Reveal answer ↓

What it is

The remainder theorem says the remainder of p(x) divided by (x - a) is simply p(a).

Answer

By the remainder theorem, the remainder when p(x) is divided by (x + 1) is p(-1). p(-1) = (-1)^3 + 3(-1)^2 + 3(-1) + 1 = -1 + 3 - 3 + 1 = 0. Since the remainder is 0, (x + 1) is a factor of p(x).

Remainder theorem: remainder = p(a) when dividing by (x - a)

  • •Remainder = p(-1)
  • •p(-1) = -1 + 3 - 3 + 1 = 0
  • •Remainder 0 -> (x + 1) is a factor

Why learn this

It checks factors of big polynomials in one step - a shortcut used all through algebra.

💡 Memory trick

Dividing by (x + 1)? Just plug in x = -1. Set the bracket to zero, then substitute.