Divide (4x⁴ + 9x³ +4x² +5x +2) by (x+2)
Answers
Solution:
By direct method
x+2)4x⁴+9x³+4x²+5x+2)4x³+x²+2x+1
⠀⠀⠀4x⁴+8x³
⠀⠀⠀(-)⠀(-)
⠀⠀__________
⠀⠀⠀⠀⠀⠀x³+4x²
⠀⠀⠀⠀⠀⠀x³+2x²
⠀⠀⠀⠀⠀(-)⠀(-)
⠀⠀______________
⠀⠀⠀⠀⠀⠀⠀⠀2x²+5x
⠀⠀⠀⠀⠀⠀⠀⠀2x²+4x
⠀⠀⠀⠀⠀⠀⠀(-)⠀⠀(-)
⠀⠀________________
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x+2
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x+2
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀(-)⠀(-)⠀
⠀⠀__________________
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀0
Quotient=4x³+x²+2x+1
Remainder=0
_______________________________
Verification:
Divided=Quotient×Divisor+Remainder
L.H.S.=4x⁴+9x³+4x²+5x+2
R.H.S.=(4x³+x²+2x+1)(x+2)+0
⠀⠀⠀⠀=4x⁴+x³+2x²+x+8x³+2x²+4x+2
⠀⠀⠀⠀=4x⁴+x³+8x³+2x²+2x²+x+4x+2
⠀⠀⠀⠀=4x⁴+9x³+4x²+5x+2
⠀⠀⠀⠀=L.H.S.
Hence, verified.
Answer:
4x³+x²+2x+1
Step-by-step explanation:
x+2)4x⁴ + 9x³ +4x² +5x +2( 4x³+x²+2x+1
4x⁴+8x³
- -
x³+4x²
x³+2x²
- -
2x²+5x
2x²+4x
- -
x+2
x+2
- -
0