# Applying Remainder Theorem, let us calculate whether the polynomial.P(x) = 4x3 + 4x2 – x – 1 is a multiple of (2x + 1) or not.

Remainder theorem says that,

f(x) is a polynomial of degree n (n ≥ 1) and ‘a’ is any real number. If f(x) is divided by (x – a), then the remainder will be f(a).

Let us solve the questions on the basis of this theorem.

Here, let f(x) = 4x3 + 4x2 – x – 1 …(i)

First, we need to find zero of the linear polynomial, (2x + 1).

To find zero,

2x + 1 = 0

2x = -1

x = - 1/2

f(x) will be multiple of (2x + 1) if f(-1/2) = 0.    P(x) = 4x3 + 4x2 – x – 1 is a multiple of (2x + 1).

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