Question

find the remainder when x^2-8x+4 is divided by 2x+1

Answer 1

Answer :

Remainder = 8¼ OR 33/4

Note :

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

★ Factor theorem :

If the remainder obtained on dividing a polynomial p(x) by (x - c) is zero ,

ie. if R = p(c) = 0 , then (x - c) is a factor of the polynomial p(x) .

If (x - c) is a factor of the polynomial p(x) , then the remainder obtained on dividing the polynomial p(x) by (x - c) is zero ,

ie. R = p(c) = 0 .

Solution :

Here ,

The given polynomial is ;

x² - 8x + 4

Let the given polynomial is p(x) ,

Thus ,

p(x) = x² - 8x + 4

We need to find the remainder obtained when p(x) is divided by (2x + 1) .

Thus ,

If 2x + 1 = 0 , then x = -½

Now ,

The remainder will be given as ;

=> R = p(-½)

=> R = (-½)² - 8•(-½) + 4

=> R = ¼ + 4 + 4

=> R = ¼ + 8

=> R = 8¼ OR 33/4

Hence ,

Remainder = 8¼ OR 33/4

Answer 2

Answer:

8¼ or 33/4

Step-by-step explanation:

2x + 1 = 0

=> x = -1/2

Remainder= (-1/2)² - 8(-1/2)+ 4

= 1/4 +4+4

=8¼ (ans)