Question

What is the remainder when the polynomial 6x2+11x−3 is divided by 2x−1?

Answer 1

Answer: 4

There are three different ways to find the remainder.  Since I don't know which lesson you are working on, I will show you all three methods.

Long Division:

           3x  +  7      

2x - 1 ) 6x² + 11x - 3

       -  (6x²  -  3x)   ↓

                    14x  - 3

                -   (14x  - 7)  

                              4    

Synthetic Division:

2x - 1 = 0   ⇒   x = $\frac{1}{2}$

$\frac{1}{2}$   | 6      11     -3

    | ↓       3     7

      6      14    4

Remainder Theorem:

2x - 1 = 0   ⇒   x = $\frac{1}{2}$

f(x) = 6x² + 11x - 3

f($\frac{1}{2}$) = 6($\frac{1}{2}$)² + 11($\frac{1}{2}$) - 3

      = 6($\frac{1}{4}$) + $\frac{11}{2}$ - 3

      = $\frac{3}{2}$ + $\frac{11}{2}$ - $\frac{6}{2}$

      = $\frac{8}{2}$

      = 4

                                     

Answer 2

remainder = 4

using long division

6x² + 11x - 3 = (2x - 1 )(3x + 7 ) + $\frac{4}{2x-1}$, that is

the remainder is 4