Q. 1 D5.0( 3 Votes )

# By applying Remainder Theorem, let us calculate and write the remainder that I shall get in every cases, when x3 – 3x2 + 2x + 5 is divided by2x + 1

Answer :

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.

When x3 – 3x2 + 2x + 5 is divided by (2x + 1).

Let f(x) = x3 – 3x2 + 2x + 5 …(1)

Now, let’s find out the zero of the linear polynomial, (2x + 1).

To find zero,

2x + 1 = 0

2x = -1

x = -1/2

This means that by remainder theorem, when x3 – 3x2 + 2x + 5 is divided by (2x + 1), the remainder comes out to be f(-1/2).

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

Remainder = f(-1/2)

Remainder

Remainder

Remainder

Remainder

Remainder

Remainder

the required remainder = 25/8

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