Question

Find if x^4+2x^3-3x^2+x-1 is devided by by x-2 by remainder theorem​

Answer 1

Answer:

Remainder = 21

Note:

★ Remainder theorem : If a polynomial p(x) is divided by (x - a) , then the remainder obtained is given by p(a).

Solution:

Here,

The given polynomial is :

x⁴ + 2x³ - 3x² + x - 1 .

Let the given polynomial be p(x) .

Thus,

p(x) = x⁴ + 2x³ - 3x² + x - 1

Now,

We need to find the remainder when the given polynomial is divided by (x - 2) .

Thus,

Using remainder theorem , the remainder (R) will be given by p(2) .

Thus,

=> R = p(2)

=> R = 2⁴ + 2•2³ - 3•2² + 2 - 1

=> R = 16 + 16 - 12 + 2 - 1

=> R = 34 - 13

=> R = 21

Hence,

The remainder is 21 .