Question

when x^6+x^4-2x^2+k is divded by 1+x^2, the remainder is 5. Find the value of k.

Answer 1

Let f(x) = x ⁶ + x ⁴ - 2 x ² + k is divided by 1 + x ²

The reminder is 5

Remember basic arithmetic : Dividend = Divisor x Quotient + Remainder.

you can use long method of dividing:

1 + x ²) x ⁶ + x ⁴ - 2 x ² + k (x⁴ - 2

         x ⁶ + x ⁴______               [ Change the symbols ]

                       - 2 x ² + k

                        - 2 x ² - 2______        [ Change the symbols ]

                                   k + 2

The reminder  is  k + 2

So  k + 2 = 5 

k = 5 - 2 = 3.

Therefore k = 3.