Please solve this. n.
Answers
Step-by-step explanation:
Solution :-
I)Given that
Dividend = x³-6x+1
Divisor = x+2
On dividing x³-6x+1 by x+2
x+2 ) x³+0x²-6x+1 ( x²-2x-2
x³+2x²
(-) (-)
__________
-2x²-6x
-2x²-4x
(+) (+)
___________
-2x+1
-2x-4
(+) (+)
_____________
5
_____________
We have ,
Dividend = x³-6x+1
Divisor = x+2
Quotient = x²-2x-2
Remainder = 5
Check:-
Divisor × Quotient + Remainder
=> (x+2)×(x²-2x-2)+5
=> x³-2x²-2x+2x²-4x-4+5
=> x³-6x+1
=> Dividend
Dividend=Divisor×Quotient+Remainder
_____________________________
2)Given that
Dividend = x³-125
Divisor = x-5
On dividing x³-125 by x-5
=> (x³-125)/(x-5)
=> (x³-5³)/(x-5)
=> (x-5)(x²+5x+25)/(x-5)
Since a³-b³ = (a-b)(a²+ab+b²)
=> x²+5x+25
or
x-5 ) x³+0x²+0x-125 ( x²+5x+25
x³-5x²
(-) (+)
____________
5x²+0x
5x²-25x
(-) (+)
______________
25x-125
25x-125
(-) (+)
________________
0
__________________
We have,
Quotient = x²+5x+25
Remainder = 0
Dividend = x³-125
Divisor = x-5
Check :-
Divisor × Quotient + Remainder
=> (x-5)(x²+5x+25)+0
=> x³+5x²+25x-5x²-25x-125+0
=> x³-125
=> Dividend
Dividend=Divisor×Quotient+Remainder
_____________________________
3)
On dividing x³-2x-21 by x-3
x-3 ) x³+0x²-2x-21 ( x²+3x+7
x³-3x²
(-) (+)
___________
3x²-2x
3x²-9x
(-) (+)
____________
7x -21
7x-21
(-) (+)
_____________
0
_____________
We have,
Quotient = x²+3x+7
Remainder = 0
Dividend = x³-2x-21
Divisor = x-3
Check:-
Divisor × Quotient + Remainder
=> (x-3)(x²+3x+7)+0
=> x³+3x²+7x-3x²-9x-21
=> x³-2x-21
=> Dividend
Dividend=Divisor×Quotient+Remainder
Used formulae:-
Dividend=Divisor×Quotient+Remainder
→ a³-b³ = (a-b)(a²+ab+b²)
Used Method :-
→ Long Division