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 by
2x + 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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