Question

What is the remainder when the polynomial 8x^2+4x−3 is divided by 2x−1?

Answer 1

The remainder of this polynomial is 1. 

Answer 2

1

Explanation:

Given: A polynomial
`8x^(2) +4x-3` is divided by another polynomial
`2x-1`

To find: Remainder when
`8x^(2) +4x-3` is divided by
`2x-1`

Solution:

To find the remainder when
`8x^(2) +4x-3` is divided by
`2x-1`

First, equate
`2x-1` with 0.

Now,
`2x-1=0`

`\implies2x=1`

`\implies x=(1)/(2)`

Now, to find the remainder put
`x=(1)/(2)` in
`8x^(2) +4x-3`

So, we have

`8*((1)/(2))^(2)+4((1)/(2) )-3`

`=8*(1)/(4) +2-3`

`=2+2-3`

`=4-3`

`=1`

Hence, the remainder is 1.