What is the remainder when the polynomial 6x² + 11x - 7 is divided by 2x - 1?

Solution :

We will apply the concepts of factorization and polynomial to find the remainder.

We have a 2-degree polynomial divided by a linear polynomial.

Now , 2x  - 1 = 0 . So by substituting x = 1 / 2 in the equation we will get the remainder.  [remainder theorem of the polynomial]

Let us substitute now x = 1 / 2 in the quadratic equation i.e. 6x² + 11x - 7 .

= 6 × (1 / 2)² + 11 × (1 / 2) - 7

= 6 / 4 + 11 / 2 - 7

= 0 

We can also perform long division

Hence, the remainder when  6x² + 11x − 7 is divided by 2x - 1 is 0 .  

What is the remainder when the polynomial 6x² + 11x - 7 is divided by 2x - 1?

Summary:

When 6x² + 11x - 7 is divided by 2x - 1 then the remainder is 0.