Q. 1 A5.0( 7 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 byx – 2

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 (x – 2).

Let f(x) = x3 – 3x2 + 2x + 5 …(1)

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

To find zero,

x – 2 = 0

x = 2

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

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

Remainder = f(2)

Remainder = (2)3 – 3(2)2 + 2(2) + 5

Remainder = 8 – 12 + 4 + 5

Remainder = 5

the required remainder = 5.

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