4. Divide the following using long division method
(a) x3 – 6x2 – x – 18 by x+2
(b) 3x3 – 26x2 + 41x – 10 by 3x – 5
(c) 8x3 – 50x2 + 83x – 90 by 2x – 9
(d) 6x3 – 17x2 + 11x – 2 by 2x – 1
Answers
Answer:
(a) x³ – 6x² – x – 18 = (x + 2)(x² -8x +15) – 48
(b) 3x³ – 26x² + 41x – 10 = (3x – 5)(x² -7x + 2)
(c) 8x³ – 50x² + 83x – 90 = (2x – 9)(4x² – 7x +10)
(d) 6x³ – 17x² + 11x – 2 = (2x – 1)(3x² -7x + 2)
Step-by-step explanation:
(a)
x+2) x³ – 6x² – x – 18 (x² - 8x +15
x³ + 2x²
---------------------------------------
-8x² – x
-8x² – 16x
-------------------------------------
15x – 18
15x + 30
-------------------------------------------------------
Reminder = -48
Hence x³ – 6x² – x – 18 = (x + 2)(x² -8x +15) – 48
Similarly, you can use long division to get other results.
I am just giving the results below.
(b)
3x³ – 26x² + 41x – 10 = (3x – 5)(x² -7x + 2)
(c)
8x³ – 50x² + 83x – 90 = (2x – 9)(4x² – 7x +10)
(d) 6x³ – 17x² + 11x – 2 = (2x – 1)(3x² -7x + 2)
Answer:
Quotient = 3x² - 7x + 2
Remainder = 0
Step-by-step explanation:
6x³ – 17x² + 11x – 2 by 2x – 1
3x² - 7x + 2
__________________________________
|
2x-1 | 6x³ – 17x² + 11x – 2
| 6x³ – 3x²
|______________
| - 14x² + 11x
| - 14x² + 7x
|------------------------------------
| 4x - 2
| 4x - 2
|---------------------------------------------
| 0
|_____________________________
Quotient = 3x² - 7x + 2
Remainder = 0