Question

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

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Answer 1

remainder = 4

using long division

6x² + 11x - 3 = (2x - 1 )(3x + 7 ) +
`(4)/(2x-1)`, that is

the remainder is 4

Answer 2

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 =
`(1)/(2)`

`(1)/(2)` | 6 11 -3

| ↓ 3 7

6 14 4

Remainder Theorem:

2x - 1 = 0 ⇒ x =
`(1)/(2)`

f(x) = 6x² + 11x - 3

f(
`(1)/(2)`) = 6(
`(1)/(2)`)² + 11(
`(1)/(2)`) - 3

= 6(
`(1)/(4)`) +
`(11)/(2)` - 3

=
`(3)/(2)` +
`(11)/(2)` -
`(6)/(2)`

=
`(8)/(2)`

= 4