remainder = 4
using long division
6x² + 11x - 3 = (2x - 1 )(3x + 7 ) + [tex]\frac{4}{2x-1}[/tex], that is
the remainder is 4
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 = [tex]\frac{1}{2}[/tex]
[tex]\frac{1}{2}[/tex] | 6 11 -3
| ↓ 3 7
6 14 4
Remainder Theorem:
2x - 1 = 0 ⇒ x = [tex]\frac{1}{2}[/tex]
f(x) = 6x² + 11x - 3
f([tex]\frac{1}{2}[/tex]) = 6([tex]\frac{1}{2}[/tex])² + 11([tex]\frac{1}{2}[/tex]) - 3
= 6([tex]\frac{1}{4}[/tex]) + [tex]\frac{11}{2}[/tex] - 3
= [tex]\frac{3}{2}[/tex] + [tex]\frac{11}{2}[/tex] - [tex]\frac{6}{2}[/tex]
= [tex]\frac{8}{2}[/tex]
= 4
