Q4 of 82 Page 126

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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