Question

when f (x) = x^4 - 3x^3 -2x^2 + x-7 , is duided by
(x-2) the remainder abtained ist​

Answer 1

Step-by-step explanation:

Given:

• f(x) = x^4 - 3x^3 - 2x^2 + x - 7 is divided by (x-2)

To find:

• remainder = ?

Solution:

We can apply remainder theorem to find the remainder.

》Remainder theorem - If p(x) is any polynomial of degree greater than or equal to 1 and p(x) is divided by the linear polynomial (x - a), then the remainder is p(a).

Step-1:

Find the zero of the polynomial x - 2

==> x - 2 = 0

==> x = 2

So, the zero of polynomial is 2.

Step-2:

Put the value of zero of the polynomial in the given polynomial f(x).

==> f(x) = x^4 - 3x^3 - 2x^2 + x - 7

==> f(2) = (2)^4 - 3 × (2)^3 - 2 × (2)^2 + 2 - 7

==> f(2) = 16 - 3 × 8 - 2 × 4 - 5

==> f(2) = 16 - 24 - 8 - 5

==> f(2) = -8 - 13

==> f(2) = -21

Hence, the remainder is -21.

Hope it helped you dear...