Question

Question 4 Unsaved What is the remainder when the polynomial 6x2+11x−3 is divided by 2x−1?

Answer 1

-1

Explanation:

Just took the test

Answer 2

To divide the polynomial
`6x^2+11x-3` by the polynomial
`2x-1,` you have to do such steps:

1 step. Multiply the polynomial
`2x-1` by
`3x`. You get the polynomial
`6x^2-3x.`

2 step. Subtract the polynomial
`6x^2-3x` fro mthe polynomial
`6x^2+11x-3:`

`6x^2+11x-3-(6x^2-3x)=6x^2+11x-3-6x^2+3x=14x-3.`

Step 3. Multiply the polynomial
`2x-1` by
`7` to get the polynomial
`14x-7.`

Step 4. Subtract the polynomial
`14x-7` from the polynomial
`14x-3:`

`14x-3-(14x-7)=14x-3-14x+7=4.`

Step 5. Write the division result:

`6x^2+11x-3=(2x-1)(3x+7)+4.`

Here the quotient is the polynomial
`3x+7` and the remainder is the polynomial
`4.`

Answer: the remainder is 4.