Question

if the remainder on dividing the polynomial 2 x power 4 minus k x ki power 2 + 5 x minus 3 k + 3 by X + 2 is 4 then find the value of k​

Answer 1

Use long division method for the given polynomials as shown below: We get the remainder as . Since, is a factor of the given polynomial, the remainder should be zero. Hence, 21+7k=0 and 2k2+8k+6=0 at the same time. k= -3 satisfies both equations. Hence, k=-3. So we can write the polynomial as Hence, the zeroes of are The above two are factors of the 4th degree polynomial as well. The other two roots of the 4th degree polynomial are roots of the quadratic