Question

1. Find the quotient and remainder using synthetic division

Answer 1

Hi ,

1 )

x - 1 ) x³ + x² - 3x + 5 ( x² + 2x - 1
**†****x³ - x²
______________
**********2x² - 3x
*********2x² - 2x
________________
************** -x + 5
************** - x + 1
_______________
****************** 4

Quotient = x² + 2x - 1

2 )

x + 3 ) 3x³ - 2x² + 7x - 5 ( 3x² - 11x + 26
********3x³ + 9x²
______________
************** - 11x² + 7x
************** -11x² - 33x
___________________
*********************** 26x - 5
*********************** 26x + 78
_____________________
************************** - 83

Quotient = 3x² - 11x + 26

Remainder = - 83

3 )

3x -2)3x³+4x² -10x+ 6(3x²+10x/3-10/9
*******3x³ - 6x²
________________
************ 10x² - 10x
*************10x² - 20x/3
___________________
******************** - 10x/3 + 6
**********************- 10x/3 - 20/3
________________________
*************************** 38/3

Quotient = 3x² + 10x/3 - 10/9

Remainder = 38/3

iv )

3x + 1 ) 3x³-4x² + 0-5(3x²-7x/3 + 7/9
********3x³ + 3x²
_______________
************ - 7x² + 0
************* -7x² - 7x/3
__________________
******************* 7x/3 - 5
*********************7x/3 + 7/9
______________________
************************ -52/9

Quotient = 3x² - 7x/3 + 7/9

Remainder = -52/9

Use same method to solve remaining

Problems.

I hope this helps you.

: )