Q. 2 C5.0( 3 Votes )

# By applying Remainder Theorem, let us calculate and write the remainders, that I shall get when the following polynomials are divided by (x – 1).4x3 + 4x2 – x – 1

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 following questions on the basis of this remainder theorem.

Let f(x) = 4x3 + 4x2 – x – 1 …(1)

When 4x3 + 4x2 – x – 1 is divided by (x – 1).

Now, let’s find out the zero of the linear polynomial, (x – 1).

To find zero,

x – 1 = 0

x = 1

This means that by remainder theorem, when 4x3 + 4x2 – x – 1 is divided by (x – 1), the remainder comes out to be f(1).

From equation (1), remainder can be calculated as,

Remainder = f(1)

Remainder = 4(1)3 + 4(1)2 – (1) – 1

Remainder = 4 + 4 – 1 – 1

Remainder = 8 – 2

Remainder = 6

the required remainder = 6

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